⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

;Task: If your language has a library or built-in functions for trigonometry, show examples of: ::* sine ::* cosine ::* tangent ::* inverses (of the above)

using the same angle in radians and degrees.

For the non-inverse functions, each radian/degree pair should use arguments that evaluate to the same angle (that is, it's not necessary to use the same angle for all three regular functions as long as the two sine calls use the same angle).

For the inverse functions, use the same number and convert its answer to radians and degrees.

If your language does not have trigonometric functions available or only has some available, write functions to calculate the functions based on any [[wp:List of trigonometric identities|known approximation or identity]].

## ACL2

{{incomplete|ACL2}} (This doesn't have the inverse functions; the Taylor series for those take too long to converge.)

(defun fac (n)
(if (zp n)
1
(* n (fac (1- n)))))

(defconst *pi-approx*
(/ 3141592653589793238462643383279
(expt 10 30)))

(include-book "arithmetic-3/floor-mod/floor-mod" :dir :system)

(defun dgt-to-str (d)
(case d
(1 "1") (2 "2") (3 "3") (4 "4") (5 "5")
(6 "6") (7 "7") (8 "8") (9 "9") (0 "0")))

(defmacro cat (&rest args)
(concatenate 'string ,@args))

(defun num-to-str-r (n)
(if (zp n)
""
(cat (num-to-str-r (floor n 10))
(dgt-to-str (mod n 10)))))

(defun num-to-str (n)
(cond ((= n 0) "0")
((< n 0) (cat "-" (num-to-str-r (- n))))
(t (num-to-str-r n))))

(declare (xargs :measure (nfix (- places lngth))))
(if (zp (- places lngth))
str
(pad-with-zeros places (cat "0" str) (1+ lngth))))

(defun as-decimal-str (r places)
(let ((before (floor r 1))
(after (floor (* (expt 10 places) (mod r 1)) 1)))
(cat (num-to-str before)
"."
(let ((afterstr (num-to-str after)))
(length afterstr))))))

(defun taylor-sine (theta terms term)
(declare (xargs :measure (nfix (- terms term))))
(if (zp (- terms term))
0
(+ (/ (*(expt -1 term) (expt theta (1+ (* 2 term))))
(fac (1+ (* 2 term))))
(taylor-sine theta terms (1+ term)))))

(defun sine (theta)
(taylor-sine (mod theta (* 2 *pi-approx*))
20 0)) ; About 30 places of accuracy

(defun cosine (theta)
(sine (+ theta (/ *pi-approx* 2))))

(defun tangent (theta)
(/ (sine theta) (cosine theta)))

(* *pi-approx* (/ deg 180)))

(defun trig-demo ()
(progn$(cw "sine of pi / 4 radians: ") (cw (as-decimal-str (sine (/ *pi-approx* 4)) 20)) (cw "~%sine of 45 degrees: ") (cw (as-decimal-str (sine (deg->rad 45)) 20)) (cw "~%cosine of pi / 4 radians: ") (cw (as-decimal-str (cosine (/ *pi-approx* 4)) 20)) (cw "~%tangent of pi / 4 radians: ") (cw (as-decimal-str (tangent (/ *pi-approx* 4)) 20)) (cw "~%")))  sine of pi / 4 radians: 0.70710678118654752440 sine of 45 degrees: 0.70710678118654752440 cosine of pi / 4 radians: 0.70710678118654752440 tangent of pi / 4 radians: 0.99999999999999999999  ## ActionScript Actionscript supports basic trigonometric and inverse trigonometric functions via the Math class, including the atan2 function, but not the hyperbolic functions. trace("Radians:"); trace("sin(Pi/4) = ", Math.sin(Math.PI/4)); trace("cos(Pi/4) = ", Math.cos(Math.PI/4)); trace("tan(Pi/4) = ", Math.tan(Math.PI/4)); trace("arcsin(0.5) = ", Math.asin(0.5)); trace("arccos(0.5) = ", Math.acos(0.5)); trace("arctan(0.5) = ", Math.atan(0.5)); trace("arctan2(-1,-2) = ", Math.atan2(-1,-2)); trace("\nDegrees") trace("sin(45) = ", Math.sin(45 * Math.PI/180)); trace("cos(45) = ", Math.cos(45 * Math.PI/180)); trace("tan(45) = ", Math.tan(45 * Math.PI/180)); trace("arcsin(0.5) = ", Math.asin(0.5)*180/Math.PI); trace("arccos(0.5) = ", Math.acos(0.5)*180/Math.PI); trace("arctan(0.5) = ", Math.atan(0.5)*180/Math.PI); trace("arctan2(-1,-2) = ", Math.atan2(-1,-2)*180/Math.PI);  ## Ada Ada provides library trig functions which default to radians along with corresponding library functions for which the cycle can be specified. The examples below specify the cycle for degrees and for radians. The output of the inverse trig functions is in units of the specified cycle (degrees or radians). with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; with Ada.Float_Text_Io; use Ada.Float_Text_Io; with Ada.Text_IO; use Ada.Text_IO; procedure Trig is Degrees_Cycle : constant Float := 360.0; Radians_Cycle : constant Float := 2.0 * Ada.Numerics.Pi; Angle_Degrees : constant Float := 45.0; Angle_Radians : constant Float := Ada.Numerics.Pi / 4.0; procedure Put (V1, V2 : Float) is begin Put (V1, Aft => 5, Exp => 0); Put (" "); Put (V2, Aft => 5, Exp => 0); New_Line; end Put; begin Put (Sin (Angle_Degrees, Degrees_Cycle), Sin (Angle_Radians, Radians_Cycle)); Put (Cos (Angle_Degrees, Degrees_Cycle), Cos (Angle_Radians, Radians_Cycle)); Put (Tan (Angle_Degrees, Degrees_Cycle), Tan (Angle_Radians, Radians_Cycle)); Put (Cot (Angle_Degrees, Degrees_Cycle), Cot (Angle_Radians, Radians_Cycle)); Put (ArcSin (Sin (Angle_Degrees, Degrees_Cycle), Degrees_Cycle), ArcSin (Sin (Angle_Radians, Radians_Cycle), Radians_Cycle)); Put (Arccos (Cos (Angle_Degrees, Degrees_Cycle), Degrees_Cycle), Arccos (Cos (Angle_Radians, Radians_Cycle), Radians_Cycle)); Put (Arctan (Y => Tan (Angle_Degrees, Degrees_Cycle)), Arctan (Y => Tan (Angle_Radians, Radians_Cycle))); Put (Arccot (X => Cot (Angle_Degrees, Degrees_Cycle)), Arccot (X => Cot (Angle_Degrees, Degrees_Cycle))); end Trig;  {{out}}  0.70711 0.70711 0.70711 0.70711 1.00000 1.00000 1.00000 1.00000 45.00000 0.78540 45.00000 0.78540 45.00000 0.78540 45.00000 0.78540  ## ALGOL 68 {{trans|C}} {{works with|ALGOL 68|Standard - no extensions to language used}} {{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}} {{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386}} main:( REAL pi = 4 * arc tan(1); # Pi / 4 is 45 degrees. All answers should be the same. # REAL radians = pi / 4; REAL degrees = 45.0; REAL temp; # sine # print((sin(radians), " ", sin(degrees * pi / 180), new line)); # cosine # print((cos(radians), " ", cos(degrees * pi / 180), new line)); # tangent # print((tan(radians), " ", tan(degrees * pi / 180), new line)); # arcsine # temp := arc sin(sin(radians)); print((temp, " ", temp * 180 / pi, new line)); # arccosine # temp := arc cos(cos(radians)); print((temp, " ", temp * 180 / pi, new line)); # arctangent # temp := arc tan(tan(radians)); print((temp, " ", temp * 180 / pi, new line)) )  {{out}}  +.707106781186548e +0 +.707106781186548e +0 +.707106781186548e +0 +.707106781186548e +0 +.100000000000000e +1 +.100000000000000e +1 +.785398163397448e +0 +.450000000000000e +2 +.785398163397448e +0 +.450000000000000e +2 +.785398163397448e +0 +.450000000000000e +2  ## ALGOL W begin % Algol W only supplies sin, cos and arctan as standard. We can define % % arcsin, arccos and tan functions using these. The standard functions % % use radians so we also provide versions that use degrees % % convert degrees to radians % real procedure toRadians( real value x ) ; pi * ( x / 180 ); % convert radians to degrees % real procedure toDegrees( real value x ) ; 180 * ( x / pi ); % tan of an angle in radians % real procedure tan( real value x ) ; sin( x ) / cos( x ); % arcsin in radians % real procedure arcsin( real value x ) ; arctan( x / sqrt( 1 - ( x * x ) ) ); % arccos in radians % real procedure arccos( real value x ) ; arctan( sqrt( 1 - ( x * x ) ) / x ); % sin of an angle in degrees % real procedure sinD( real value x ) ; sin( toRadians( x ) ); % cos of an angle in degrees % real procedure cosD( real value x ) ; cos( toRadians( x ) ); % tan of an angle in degrees % real procedure tanD( real value x ) ; tan( toRadians( x ) ); % arctan in degrees % real procedure arctanD( real value x ) ; toDegrees( arctan( x ) ); % arcsin in degrees % real procedure arcsinD( real value x ) ; toDegrees( arcsin( x ) ); % arccos in degrees % real procedure arccosD( real value x ) ; toDegrees( arccos( x ) ); % test the procedures % begin real piOver4, piOver3, oneOverRoot2, root3Over2; piOver3 := pi / 3; piOver4 := pi / 4; oneOverRoot2 := 1.0 / sqrt( 2 ); root3Over2 := sqrt( 3 ) / 2; r_w := 12; r_d := 5; r_format := "A"; s_w := 0; % set output format % write( "PI/4: ", piOver4, " 1/root(2): ", oneOverRoot2 ); write(); write( "sin 45 degrees: ", sinD( 45 ), " sin pi/4 radians: ", sin( piOver4 ) ); write( "cos 45 degrees: ", cosD( 45 ), " cos pi/4 radians: ", cos( piOver4 ) ); write( "tan 45 degrees: ", tanD( 45 ), " tan pi/4 radians: ", tan( piOver4 ) ); write(); write( "arcsin( sin( pi/4 radians ) ): ", arcsin( sin( piOver4 ) ) ); write( "arccos( cos( pi/4 radians ) ): ", arccos( cos( piOver4 ) ) ); write( "arctan( tan( pi/4 radians ) ): ", arctan( tan( piOver4 ) ) ); write(); write( "PI/3: ", piOver4, " root(3)/2: ", root3Over2 ); write(); write( "sin 60 degrees: ", sinD( 60 ), " sin pi/3 radians: ", sin( piOver3 ) ); write( "cos 60 degrees: ", cosD( 60 ), " cos pi/3 radians: ", cos( piOver3 ) ); write( "tan 60 degrees: ", tanD( 60 ), " tan pi/3 radians: ", tan( piOver3 ) ); write(); write( "arcsin( sin( 60 degrees ) ): ", arcsinD( sinD( 60 ) ) ); write( "arccos( cos( 60 degrees ) ): ", arccosD( cosD( 60 ) ) ); write( "arctan( tan( 60 degrees ) ): ", arctanD( tanD( 60 ) ) ); end end.  {{out}}  PI/4: 0.78539 1/root(2): 0.70710 sin 45 degrees: 0.70710 sin pi/4 radians: 0.70710 cos 45 degrees: 0.70710 cos pi/4 radians: 0.70710 tan 45 degrees: 1.00000 tan pi/4 radians: 1.00000 arcsin( sin( pi/4 radians ) ): 0.78539 arccos( cos( pi/4 radians ) ): 0.78539 arctan( tan( pi/4 radians ) ): 0.78539 PI/3: 0.78539 root(3)/2: 0.86602 sin 60 degrees: 0.86602 sin pi/3 radians: 0.86602 cos 60 degrees: 0.50000 cos pi/3 radians: 0.50000 tan 60 degrees: 1.73205 tan pi/3 radians: 1.73205 arcsin( sin( 60 degrees ) ): 60.00000 arccos( cos( 60 degrees ) ): 60.00000 arctan( tan( 60 degrees ) ): 60.00000  ## Arturo {{trans|C}} pi 4*$(atan 1)

degrees 45.0

"sine"
print $(sin radians) + " " +$(sin degrees*pi/180)

"cosine"
print $(cos radians) + " " +$(cos degrees*pi/180)

"tangent"
print $(tan radians) + " " +$(tan degrees*pi/180)

"arcsine"
print $(asin$(sin radians)) + " " +$(asin$(sin radians))*180/pi

"arccosine"
print $(acos$(cos radians)) + " " +$(acos$(cos radians))*180/pi

"arctangent"
print $(atan$(tan radians)) + " " +$(atan$(tan radians))*180/pi


{{out}}

sine
0.707107 0.707107
cosine
0.707107 0.707107
tangent
1 1
arcsine
0.785398 45
arccosine
0.785398 45
arctangent
0.785398 45


## AutoHotkey

{{trans|C}}

pi := 4 * atan(1)
degrees := 45.0
result .= "n" . sin(radians) . "     " . sin(degrees * pi / 180)
result .= "n" . cos(radians) . "     " . cos(degrees * pi / 180)
result .= "n" . tan(radians) . "     " . tan(degrees * pi / 180)

result .= "n" . temp . "     " . temp * 180 / pi

result .= "n" . temp . "     " . temp * 180 / pi

result .= "n" . temp . "     " . temp * 180 / pi

msgbox % result
/* output
---------------------------
trig.ahk
---------------------------
0.707107     0.707107
0.707107     0.707107
1.000000     1.000000
0.785398     45.000000
0.785398     45.000000
0.785398     45.000000
*/


## Autolisp

Autolisp provides (sin x) (cos x) (tan x) and (atan x). Function arguments are expressed in radians.


(defun deg_to_rad (deg)(* PI (/ deg 180.0)))

(defun asin (x)
(cond
((and(> x -1.0)(< x 1.0)) (atan (/ x (sqrt (- 1.0 (* x x))))))
((= x -1.0) (* -1.0 (/ pi 2)))
((= x 1) (/ pi 2))
)
)

(defun acos (x)
(cond
((and(>= x -1.0)(<= x 1.0)) (-(* pi 0.5) (asin x)))
)
)

(list
(list "cos PI/6" (cos (/ pi 6)) "cos 30 deg" (cos (deg_to_rad 30)))
(list "sin PI/4" (sin (/ pi 4)) "sin 45 deg" (sin (deg_to_rad 45)))
(list "tan PI/3" (tan (/ pi 3))"tan 60 deg" (tan (deg_to_rad 60)))
(list "acos 1/2 rad" (acos (/ 1 2.0)) "acos 1/2 rad (deg)" (rad_to_deg (acos (/ 1 2.0))))
(list "atan pi/12" (atan (/ pi 12)) "atan 15 deg" (rad_to_deg(atan(deg_to_rad 15))))
)



{{out}}


(("cos PI/6 rad" 0.866025 "cos 30 deg" 0.866025)
("sin PI/4 rad" 0.707107 "sin 45 deg" 0.707107)
("tan PI/3 rad" 1.73205 " tan 60 deg" 1.73205)
("atan pi/12 rad" 0.256053 "atan 15 deg" 14.6707))



## AWK

Awk only provides sin(), cos() and atan2(), the three bare necessities for trigonometry. They all use radians. To calculate the other functions, we use these three trigonometric identities:

{|class="wikitable" ! tangent ! arcsine ! arccosine |- | $\tan \theta = \frac\left\{\sin \theta\right\}\left\{\cos \theta\right\}$ | $\tan\left(\arcsin y\right) = \frac\left\{y\right\}\left\{\sqrt\left\{1 - y^2\right\}\right\}$ | $\tan\left(\arccos x\right) = \frac\left\{\sqrt\left\{1 - x^2\right\}\right\}\left\{x\right\}$ |}

With the magic of atan2(), arcsine of ''y'' is just atan2(y, sqrt(1 - y * y)), and arccosine of ''x'' is just atan2(sqrt(1 - x * x), x). This magic handles the angles ''arcsin(-1)'', ''arcsin 1'' and ''arccos 0'' that have no tangent. This magic also picks the angle in the correct range, so ''arccos(-1/2)'' is ''2pi/3'' and not some wrong answer like ''-pi/3'' (though ''tan(2pi/3) = tan(-pi/3) = -sqrt(3)''.)

atan2(y, x) actually computes the angle of the point ''(x, y)'', in the range ''[-pi, pi]''. When x > 0, this angle is the principle arctangent of ''y/x'', in the range ''(-pi/2, pi/2)''. The calculations for arcsine and arccosine use points on the unit circle at ''x2 + y2 = 1''. To calculate arcsine in the range ''[-pi/2, pi/2]'', we take the angle of points on the half-circle ''x = sqrt(1 - y2)''. To calculate arccosine in the range ''[0, pi]'', we take the angle of points on the half-circle ''y = sqrt(1 - x2)''.

# tan(x) = tangent of x
function tan(x) {
return sin(x) / cos(x)
}

# asin(y) = arcsine of y, domain [-1, 1], range [-pi/2, pi/2]
function asin(y) {
return atan2(y, sqrt(1 - y * y))
}

# acos(x) = arccosine of x, domain [-1, 1], range [0, pi]
function acos(x) {
return atan2(sqrt(1 - x * x), x)
}

# atan(y) = arctangent of y, range (-pi/2, pi/2)
function atan(y) {
return atan2(y, 1)
}

BEGIN {
pi = atan2(0, -1)
degrees = pi / 180

print "  sin(-pi / 6) =", sin(-pi / 6)
print "  cos(3 * pi / 4) =", cos(3 * pi / 4)
print "  tan(pi / 3) =", tan(pi / 3)
print "  asin(-1 / 2) =", asin(-1 / 2)
print "  acos(-sqrt(2) / 2) =", acos(-sqrt(2) / 2)
print "  atan(sqrt(3)) =", atan(sqrt(3))

print "Using degrees:"
print "  sin(-30) =", sin(-30 * degrees)
print "  cos(135) =", cos(135 * degrees)
print "  tan(60) =", tan(60 * degrees)
print "  asin(-1 / 2) =", asin(-1 / 2) / degrees
print "  acos(-sqrt(2) / 2) =", acos(-sqrt(2) / 2) / degrees
print "  atan(sqrt(3)) =", atan(sqrt(3)) / degrees
}


{{out}}

Using radians:
sin(-pi / 6) = -0.5
cos(3 * pi / 4) = -0.707107
tan(pi / 3) = 1.73205
asin(-1 / 2) = -0.523599
acos(-sqrt(2) / 2) = 2.35619
atan(sqrt(3)) = 1.0472
Using degrees:
sin(-30) = -0.5
cos(135) = -0.707107
tan(60) = 1.73205
asin(-1 / 2) = -30
acos(-sqrt(2) / 2) = 135
atan(sqrt(3)) = 60


## Axe

Axe implements sine, cosine, and inverse tangent natively. One period is [0, 256) and the results are [-127, 127] for maximum precision.

The inverse tangent takes dX and dY parameters, rather than a single argument. This is because it is most often used to calculate angles.

Disp sin(43)▶Dec,i
Disp cos(43)▶Dec,i
Disp tan⁻¹(10,10)▶Dec,i


{{out}}

  113
68
32


Below is the worked out math.

On a period of 256, an argument of 43 is equivalent to $\frac\left\{\pi\right\}\left\{3\right\} * \frac\left\{128\right\}\left\{\pi\right\}$.

Furthermore, $127*\frac\left\{\sqrt\left\{3\right\}\right\}\left\{2\right\} \approx 111$ and $127*\frac\left\{1\right\}\left\{2\right\} \approx 64$.

So $\sin\left\{43\right\} \approx 113$ and $\cos\left\{43\right\} \approx 68$. Axe uses approximations to calculate the trigonometric functions.

dX and dY values of 10 mean that the angle between them should be $\frac\left\{\pi\right\}\left\{4\right\}$. Indeed, the result $\tan^\left\{-1\right\}\left\{\left(10, 10\right)\right\} = 32 = \frac\left\{128\right\}\left\{4\right\}$.

## BaCon

' Trigonometric functions in BaCon use Radians for input values

FOR v$IN "0, 10, 45, 90, 190.5" d = VAL(v$) * 1.0

PRINT "Sine: ", d, " degrees (or ", r, " radians) is ", SIN(r)
PRINT "Cosine: ", d, " degrees (or ", r, " radians) is ", COS(r)
PRINT "Tangent: ", d, " degrees (or ", r, " radians) is ", TAN(r)
PRINT
PRINT "Arc Sine: ", SIN(r), " is ", DEG(ASIN(SIN(r))), " degrees (or ", ASIN(SIN(r)), " radians)"
PRINT "Arc CoSine: ", COS(r), " is ", DEG(ACOS(COS(r))), " degrees (or ", ACOS(COS(r)), " radians)"
PRINT "Arc Tangent: ", TAN(r), " is ", DEG(ATN(TAN(r))), " degrees (or ", ATN(TAN(r)), " radians)"
PRINT
NEXT


{{out}}

prompt$bacon -q trigonometric-functions.bac ... Done, program 'trigonometric-functions' ready. prompt$ ./trigonometric-functions
Sine: 0 degrees (or 0 radians) is 0
Cosine: 0 degrees (or 0 radians) is 1
Tangent: 0 degrees (or 0 radians) is 0

Arc Sine: 0 is 0 degrees (or 0 radians)
Arc CoSine: 1 is 0 degrees (or 0 radians)
Arc Tangent: 0 is 0 degrees (or 0 radians)

Sine: 10 degrees (or 0.174533 radians) is 0.173648
Cosine: 10 degrees (or 0.174533 radians) is 0.984808
Tangent: 10 degrees (or 0.174533 radians) is 0.176327

Arc Sine: 0.173648 is 10 degrees (or 0.174533 radians)
Arc CoSine: 0.984808 is 10 degrees (or 0.174533 radians)
Arc Tangent: 0.176327 is 10 degrees (or 0.174533 radians)

Sine: 45 degrees (or 0.785398 radians) is 0.707107
Cosine: 45 degrees (or 0.785398 radians) is 0.707107
Tangent: 45 degrees (or 0.785398 radians) is 1

Arc Sine: 0.707107 is 45 degrees (or 0.785398 radians)
Arc CoSine: 0.707107 is 45 degrees (or 0.785398 radians)
Arc Tangent: 1 is 45 degrees (or 0.785398 radians)

Sine: 90 degrees (or 1.5708 radians) is 1
Cosine: 90 degrees (or 1.5708 radians) is 6.12323e-17
Tangent: 90 degrees (or 1.5708 radians) is 16331239353195370

Arc Sine: 1 is 90 degrees (or 1.5708 radians)
Arc CoSine: 6.12323e-17 is 90 degrees (or 1.5708 radians)
Arc Tangent: 16331239353195370 is 90 degrees (or 1.5708 radians)

Sine: 190.5 degrees (or 3.32485 radians) is -0.182236
Cosine: 190.5 degrees (or 3.32485 radians) is -0.983255
Tangent: 190.5 degrees (or 3.32485 radians) is 0.185339

Arc Sine: -0.182236 is -10.5 degrees (or -0.18326 radians)
Arc CoSine: -0.983255 is 169.5 degrees (or 2.95833 radians)
Arc Tangent: 0.185339 is 10.5 degrees (or 0.18326 radians)


## BASIC

{{works with|QuickBasic|4.5}} QuickBasic 4.5 does not have arcsin and arccos built in. They are defined by identities found [[wp:Arctan#Relationships_among_the_inverse_trigonometric_functions|here]].

pi = 3.141592653589793#
radians = pi / 4 'a.k.a. 45 degrees
degrees = 45 * pi / 180 'convert 45 degrees to radians once
PRINT SIN(radians) + " " + SIN(degrees) 'sine
PRINT COS(radians) + " " + COS(degrees) 'cosine
PRINT TAN(radians) + " " + TAN (degrees) 'tangent
'arcsin
arcsin = ATN(thesin / SQR(1 - thesin ^ 2))
PRINT arcsin + " " + arcsin * 180 / pi
'arccos
arccos = 2 * ATN(SQR(1 - thecos ^ 2) / (1 + thecos))
PRINT arccos + " " + arccos * 180 / pi
PRINT ATN(TAN(radians)) + " " + ATN(TAN(radians)) * 180 / pi 'arctan


=

## BBC BASIC

=

      @% = &90F : REM set column width

angle_degrees = 36

number = 0.6

PRINT ASN(number), DEG(ASN(number))
PRINT ACS(number), DEG(ACS(number))
PRINT ATN(number), DEG(ATN(number))


==={{header|IS-BASIC}}=== 100 LET DG=DEG(PI/4) 110 OPTION ANGLE DEGREES 120 PRINT SIN(DG) 130 PRINT COS(DG) 140 PRINT TAN(DG) 150 PRINT ASIN(SIN(DG)) 160 PRINT ACOS(COS(DG)) 170 PRINT ATN(TAN(DG)) 180 LET RD=RAD(45) 190 OPTION ANGLE RADIANS 200 PRINT SIN(RD) 210 PRINT COS(RD) 220 PRINT TAN(RD) 230 PRINT ASIN(SIN(RD)) 240 PRINT ACOS(COS(RD)) 250 PRINT ATN(TAN(RD))



## bc

{{trans|AWK}}

bc
/* t(x) = tangent of x */
define t(x) {
return s(x) / c(x)
}

/* y(y) = arcsine of y, domain [-1, 1], range [-pi/2, pi/2] */
define y(y) {
/* Handle angles with no tangent. */
if (y == -1) return -2 * a(1)  /* -pi/2 */
if (y == 1) return 2 * a(1)    /* pi/2 */

/* Tangent of angle is y / x, where x^2 + y^2 = 1. */
return a(y / sqrt(1 - y * y))
}

/* x(x) = arccosine of x, domain [-1, 1], range [0, pi] */
define x(x) {
auto a

/* Handle angle with no tangent. */
if (x == 0) return 2 * a(1)  /* pi/2 */

/* Tangent of angle is y / x, where x^2 + y^2 = 1. */
a = a(sqrt(1 - x * x) / x)
if (a < 0) {
return a + 4 * a(1)  /* add pi */
} else {
return a
}
}

scale = 50
p = 4 * a(1)  /* pi */
d = p / 180   /* one degree in radians */

"
"  sin(-pi / 6) = "; s(-p / 6)
"  cos(3 * pi / 4) = "; c(3 * p / 4)
"  tan(pi / 3) = "; t(p / 3)
"  asin(-1 / 2) = "; y(-1 / 2)
"  acos(-sqrt(2) / 2) = "; x(-sqrt(2) / 2)
"  atan(sqrt(3)) = "; a(sqrt(3))

"Using degrees:
"
"  sin(-30) = "; s(-30 * d)
"  cos(135) = "; c(135 * d)
"  tan(60) = "; t(60 * d)
"  asin(-1 / 2) = "; y(-1 / 2) / d
"  acos(-sqrt(2) / 2) = "; x(-sqrt(2) / 2) / d
"  atan(sqrt(3)) = "; a(sqrt(3)) / d

quit


{{out}}

Using radians:
sin(-pi / 6) = -.49999999999999999999999999999999999999999999999999
cos(3 * pi / 4) = -.70710678118654752440084436210484903928483593768845
tan(pi / 3) = 1.73205080756887729352744634150587236694280525381032
asin(-1 / 2) = -.52359877559829887307710723054658381403286156656251
acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953131
atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312503
Using degrees:
sin(-30) = -.49999999999999999999999999999999999999999999999981
cos(135) = -.70710678118654752440084436210484903928483593768778
tan(60) = 1.73205080756887729352744634150587236694280525380865
asin(-1 / 2) = -30.00000000000000000000000000000000000000000000001203
acos(-sqrt(2) / 2) = 135.00000000000000000000000000000000000000000000005500
atan(sqrt(3)) = 60.00000000000000000000000000000000000000000000002463


## C

#include <math.h>
#include <stdio.h>

int main() {
double pi = 4 * atan(1);
/*Pi / 4 is 45 degrees. All answers should be the same.*/
double radians = pi / 4;
double degrees = 45.0;
double temp;
/*sine*/
printf("%f %f\n", sin(radians), sin(degrees * pi / 180));
/*cosine*/
printf("%f %f\n", cos(radians), cos(degrees * pi / 180));
/*tangent*/
printf("%f %f\n", tan(radians), tan(degrees * pi / 180));
/*arcsine*/
printf("%f %f\n", temp, temp * 180 / pi);
/*arccosine*/
printf("%f %f\n", temp, temp * 180 / pi);
/*arctangent*/
printf("%f %f\n", temp, temp * 180 / pi);

return 0;
}


{{out}}


0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45.000000
0.785398 45.000000
0.785398 45.000000



## C++

#include <iostream>
#include <cmath>

#ifdef M_PI // defined by all POSIX systems and some non-POSIX ones
double const pi = M_PI;
#else
double const pi = 4*std::atan(1);
#endif

double const degree = pi/180;

int main()
{
std::cout << "
\n";
std::cout << "sin(pi/3) = " << std::sin(pi/3) << "\n";
std::cout << "cos(pi/3) = " << std::cos(pi/3) << "\n";
std::cout << "tan(pi/3) = " << std::tan(pi/3) << "\n";
std::cout << "arcsin(1/2) = " << std::asin(0.5) << "\n";
std::cout << "arccos(1/2) = " << std::acos(0.5) << "\n";
std::cout << "arctan(1/2) = " << std::atan(0.5) << "\n";

std::cout << "\n
###  degrees
\n";
std::cout << "sin(60°) = " << std::sin(60*degree) << "\n";
std::cout << "cos(60°) = " << std::cos(60*degree) << "\n";
std::cout << "tan(60°) = " << std::tan(60*degree) << "\n";
std::cout << "arcsin(1/2) = " << std::asin(0.5)/degree << "°\n";
std::cout << "arccos(1/2) = " << std::acos(0.5)/degree << "°\n";
std::cout << "arctan(1/2) = " << std::atan(0.5)/degree << "°\n";

return 0;
}


## C#

using System;

namespace RosettaCode {
class Program {
static void Main(string[] args) {
Console.WriteLine("
");
Console.WriteLine("sin (pi/3) = {0}", Math.Sin(Math.PI / 3));
Console.WriteLine("cos (pi/3) = {0}", Math.Cos(Math.PI / 3));
Console.WriteLine("tan (pi/3) = {0}", Math.Tan(Math.PI / 3));
Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5));
Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5));
Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5));
Console.WriteLine("");
Console.WriteLine("
###  degrees
");
Console.WriteLine("sin (60) = {0}", Math.Sin(60 * Math.PI / 180));
Console.WriteLine("cos (60) = {0}", Math.Cos(60 * Math.PI / 180));
Console.WriteLine("tan (60) = {0}", Math.Tan(60 * Math.PI / 180));
Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5) * 180/ Math.PI);
Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5) * 180 / Math.PI);
Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5) * 180 / Math.PI);

}
}
}


## Clojure

{{trans|fortran}}

(ns user
(:require [clojure.contrib.generic.math-functions :as generic]))

;(def pi Math/PI)
(def pi (* 4 (atan 1)))
(def dtor (/ pi 180))
(def rtod (/ 180 pi))
(def degrees 45)

(println (str (sin radians) " " (sin (* degrees dtor))))
(println (str (cos radians) " " (cos (* degrees dtor))))
(println (str (tan radians) " " (tan (* degrees dtor))))
(println (str (asin (sin radians) ) " " (* (asin (sin (* degrees dtor))) rtod)))
(println (str (acos (cos radians) ) " " (* (acos (cos (* degrees dtor))) rtod)))
(println (str (atan (tan radians) ) " " (* (atan (tan (* degrees dtor))) rtod)))


{{out}} (matches that of Java) 0.7071067811865475 0.7071067811865475 0.7071067811865476 0.7071067811865476 0.9999999999999999 0.9999999999999999 0.7853981633974482 44.99999999999999 0.7853981633974483 45.0 0.7853981633974483 45.0

## COBOL

       IDENTIFICATION DIVISION.
PROGRAM-ID. Trig.

DATA DIVISION.
WORKING-STORAGE SECTION.
01  Pi-Third   USAGE COMP-2.
01  Degree     USAGE COMP-2.

01  60-Degrees USAGE COMP-2.

01  Result     USAGE COMP-2.

PROCEDURE DIVISION.
COMPUTE Pi-Third = FUNCTION PI / 3

DISPLAY "  Sin(π / 3)  = " FUNCTION SIN(Pi-Third)
DISPLAY "  Cos(π / 3)  = " FUNCTION COS(Pi-Third)
DISPLAY "  Tan(π / 3)  = " FUNCTION TAN(Pi-Third)
DISPLAY "  Asin(0.5)   = " FUNCTION ASIN(0.5)
DISPLAY "  Acos(0.5)   = " FUNCTION ACOS(0.5)
DISPLAY "  Atan(0.5)   = " FUNCTION ATAN(0.5)

COMPUTE Degree = FUNCTION PI / 180
COMPUTE 60-Degrees = Degree * 60

DISPLAY "Degrees:"
DISPLAY "  Sin(60°)  = " FUNCTION SIN(60-Degrees)
DISPLAY "  Cos(60°)  = " FUNCTION COS(60-Degrees)
DISPLAY "  Tan(60°)  = " FUNCTION TAN(60-Degrees)
COMPUTE Result = FUNCTION ASIN(0.5) / 60
DISPLAY "  Asin(0.5) = " Result
COMPUTE Result = FUNCTION ACOS(0.5) / 60
DISPLAY "  Acos(0.5) = " Result
COMPUTE Result = FUNCTION ATAN(0.5) / 60
DISPLAY "  Atan(0.5) = " Result

GOBACK
.


{{out}}


Sin(π / 3)  = +0.86602540368613976
Cos(π / 3)  = +0.50000000017025856
Tan(π / 3)  = 1.732050806782486241
Asin(0.5) = +0.52359877559829897
Acos(0.5) = 1.04719755119659785
Atan(0.5) = +0.52359877559829897
Degrees:
Sin(60°)  = +0.86602538768613932
Cos(60°)  = +0.50000002788307131
Tan(60°)  = 1.732050678782493636
Asin(0.5) = 0.008726645999999999
Acos(0.5) = 0.017453291999999999
Atan(0.5) = 0.007727460000000000



## Common Lisp

(defun deg->rad (x) (* x (/ pi 180)))
(defun rad->deg (x) (* x (/ 180 pi)))

(mapc (lambda (x) (format t "~s => ~s~%" x (eval x)))
'((sin (/ pi 4))
(cos (/ pi 6))
(tan (/ pi 3))
(asin 1)
(acos 1/2)
(atan 15)


## D

{{trans|C}}

void main() {
import std.stdio, std.math;

enum degrees = 45.0L;
enum t0 = degrees * PI / 180.0L;
writeln("Reference:  0.7071067811865475244008");
writefln("Sine:       %.20f  %.20f", PI_4.sin, t0.sin);
writefln("Cosine:     %.20f  %.20f", PI_4.cos, t0.cos);
writefln("Tangent:    %.20f  %.20f", PI_4.tan, t0.tan);

writeln;
writeln("Reference:  0.7853981633974483096156");
immutable real t1 = PI_4.sin.asin;
writefln("Arcsine:    %.20f %.20f", t1, t1 * 180.0L / PI);

immutable real t2 = PI_4.cos.acos;
writefln("Arccosine:  %.20f %.20f", t2, t2 * 180.0L / PI);

immutable real t3 = PI_4.tan.atan;
writefln("Arctangent: %.20f %.20f", t3, t3 * 180.0L / PI);
}


{{out}}

Reference:  0.7071067811865475244008
Sine:       0.70710678118654752442  0.70710678118654752442
Cosine:     0.70710678118654752438  0.70710678118654752438
Tangent:    1.00000000000000000000  1.00000000000000000000

Reference:  0.7853981633974483096156
Arcsine:    0.78539816339744830970 45.00000000000000000400
Arccosine:  0.78539816339744830961 45.00000000000000000000
Arctangent: 0.78539816339744830961 45.00000000000000000000


## E

{{trans|ALGOL 68}}

def pi := (-1.0).acos()

def radians := pi / 4.0
def degrees := 45.0

def d2r := (pi/180).multiply
def r2d := (180/pi).multiply

println($\${radians.sin()} ${d2r(degrees).sin()}${radians.cos()} ${d2r(degrees).cos()}${radians.tan()} ${d2r(degrees).tan()}${def asin := radians.sin().asin()} ${r2d(asin)}${def acos := radians.cos().acos()} ${r2d(acos)}${def atan := radians.tan().atan()} {r2d(atan)} )  {{out}} 0.7071067811865475 0.7071067811865475 0.7071067811865476 0.7071067811865476 0.9999999999999999 0.9999999999999999 0.7853981633974482 44.99999999999999 0.7853981633974483 45.0 0.7853981633974483 45.0 ## Elena {{trans|C++}} ELENA 4.x: import system'math; import extensions; public program() { console.printLine("Radians:"); console.printLine("sin(π/3) = ",(Pi_value/3).sin()); console.printLine("cos(π/3) = ",(Pi_value/3).cos()); console.printLine("tan(π/3) = ",(Pi_value/3).tan()); console.printLine("arcsin(1/2) = ",0.5r.arcsin()); console.printLine("arccos(1/2) = ",0.5r.arccos()); console.printLine("arctan(1/2) = ",0.5r.arctan()); console.printLine(); console.printLine("Degrees:"); console.printLine("sin(60º) = ",60.0r.Radian.sin()); console.printLine("cos(60º) = ",60.0r.Radian.cos()); console.printLine("tan(60º) = ",60.0r.Radian.tan()); console.printLine("arcsin(1/2) = ",0.5r.arcsin().Degree,"º"); console.printLine("arccos(1/2) = ",0.5r.arccos().Degree,"º"); console.printLine("arctan(1/2) = ",0.5r.arctan().Degree,"º"); console.readChar() }  ## Elixir {{trans|Erlang}} iex(61)> deg = 45 45 iex(62)> rad = :math.pi / 4 0.7853981633974483 iex(63)> :math.sin(deg * :math.pi / 180) == :math.sin(rad) true iex(64)> :math.cos(deg * :math.pi / 180) == :math.cos(rad) true iex(65)> :math.tan(deg * :math.pi / 180) == :math.tan(rad) true iex(66)> temp = :math.acos(:math.cos(rad)) 0.7853981633974483 iex(67)> temp * 180 / :math.pi == deg true iex(68)> temp = :math.atan(:math.tan(rad)) 0.7853981633974483 iex(69)> temp * 180 / :math.pi == deg true  ## Erlang {{trans|C}}  Deg=45. Rad=math:pi()/4. math:sin(Deg * math:pi() / 180)==math:sin(Rad).  {{out}} true  math:cos(Deg * math:pi() / 180)==math:cos(Rad).  {{out}} true  math:tan(Deg * math:pi() / 180)==math:tan(Rad).  {{out}} true  Temp = math:acos(math:cos(Rad)). Temp * 180 / math:pi()==Deg.  {{out}} true  Temp = math:atan(math:tan(Rad)). Temp * 180 / math:pi()==Deg.  {{out}} true ## Factor USING: kernel math math.constants math.functions math.trig prettyprint ; pi 4 / 45 deg>rad [ sin ] [ cos ] [ tan ] [ [ . ] compose dup compose ] tri@ 2tri .5 [ asin ] [ acos ] [ atan ] tri [ dup rad>deg [ . ] bi@ ] tri@  ## Fantom Fantom's Float library includes all six trigonometric functions, which assume the number is in radians. Methods are provided to convert: toDegrees and toRadians.  class Main { public static Void main () { Float r := Float.pi / 4 echo (r.sin) echo (r.cos) echo (r.tan) echo (r.asin) echo (r.acos) echo (r.atan) // and from degrees echo (45.0f.toRadians.sin) echo (45.0f.toRadians.cos) echo (45.0f.toRadians.tan) echo (45.0f.toRadians.asin) echo (45.0f.toRadians.acos) echo (45.0f.toRadians.atan) } }  ## Forth 45e pi f* 180e f/ \ radians cr fdup fsin f. \ also available: fsincos ( r -- sin cos ) cr fdup fcos f. cr fdup ftan f. cr fdup fasin f. cr fdup facos f. cr fatan f. \ also available: fatan2 ( r1 r2 -- atan[r1/r2] )  ## Fortran Trigonometic functions expect arguments in radians so degrees require conversion PROGRAM Trig REAL pi, dtor, rtod, radians, degrees pi = 4.0 * ATAN(1.0) dtor = pi / 180.0 rtod = 180.0 / pi radians = pi / 4.0 degrees = 45.0 WRITE(*,*) SIN(radians), SIN(degrees*dtor) WRITE(*,*) COS(radians), COS(degrees*dtor) WRITE(*,*) TAN(radians), TAN(degrees*dtor) WRITE(*,*) ASIN(SIN(radians)), ASIN(SIN(degrees*dtor))*rtod WRITE(*,*) ACOS(COS(radians)), ACOS(COS(degrees*dtor))*rtod WRITE(*,*) ATAN(TAN(radians)), ATAN(TAN(degrees*dtor))*rtod END PROGRAM Trig  {{out}} 0.707107 0.707107 0.707107 0.707107 1.00000 1.00000 0.785398 45.0000 0.785398 45.0000 0.785398 45.0000 The following trigonometric functions are also available  ATAN2(y,x) ! Arctangent(y/x), ''-pi < result <= +pi'' SINH(x) ! Hyperbolic sine COSH(x) ! Hyperbolic cosine TANH(x) ! Hyperbolic tangent  But, for those with access to fatter Fortran function libraries, trigonometrical functions working in degrees are also available.  Calculate various trigonometric functions from the Fortran library. INTEGER BIT(32),B,IP !Stuff for bit fiddling. INTEGER ENUFF,I !Step through the test angles. PARAMETER (ENUFF = 17) !A selection of special values. INTEGER ANGLE(ENUFF) !All in whole degrees. DATA ANGLE/0,30,45,60,90,120,135,150,180, !Here they are. 1 210,225,240,270,300,315,330,360/ !Thus check angle folding. REAL PI,DEG2RAD !Special numbers. REAL D,R,FD,FR,AD,AR !Degree, Radian, F(D), F(R), inverses. PI = 4*ATAN(1.0) !SINGLE PRECISION 1·0. DEG2RAD = PI/180 !Limited precision here too for a transcendental number. Case the first: sines. WRITE (6,10) ("Sin", I = 1,4) !Supply some names. 10 FORMAT (" Deg.",A7,"(Deg)",A7,"(Rad) Rad - Deg", !Ah, layout. 1 6X,"Arc",A3,"D",6X,"Arc",A3,"R",9X,"Diff") DO I = 1,ENUFF !Step through the test values. D = ANGLE(I) !The angle in degrees, in floating point. R = D*DEG2RAD !Approximation, in radians. FD = SIND(D); AD = ASIND(FD) !Functions working in degrees. FR = SIN(R); AR = ASIN(FR)/DEG2RAD !Functions working in radians. WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD !Results. 11 FORMAT (I4,":",3F12.8,3F13.7) !Ah, alignment with FORMAT 10... END DO !On to the next test value. Case the second: cosines. WRITE (6,10) ("Cos", I = 1,4) DO I = 1,ENUFF D = ANGLE(I) R = D*DEG2RAD FD = COSD(D); AD = ACOSD(FD) FR = COS(R); AR = ACOS(FR)/DEG2RAD WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD END DO Case the third: tangents. WRITE (6,10) ("Tan", I = 1,4) DO I = 1,ENUFF D = ANGLE(I) R = D*DEG2RAD FD = TAND(D); AD = ATAND(FD) FR = TAN(R); AR = ATAN(FR)/DEG2RAD WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD END DO WRITE (6,*) "...Special deal for 90 degrees..." D = 90 R = D*DEG2RAD FD = TAND(D); AD = ATAND(FD) FR = TAN(R); AR = ATAN(FR)/DEG2RAD WRITE (6,*) "TanD =",FD,"Atan =",AD WRITE (6,*) "TanR =",FR,"Atan =",AR Convert PI to binary... PI = PI - 3 !I know it starts with three, and I need the fractional part. BIT(1:2) = 1 !So, the binary is 11. something. B = 2 !Two bits known. DO I = 1,26 !For single precision, more than enough additional bits. PI = PI*2 !Hoist a bit to the hot spot. IP = PI !The integral part. PI = PI - IP !Remove it from the work in progress. B = B + 1 !Another bit bitten. BIT(B) = IP !Place it. END DO !On to the next. WRITE (6,20) BIT(1:B) !Reveal the bits. 20 FORMAT (" Pi ~ ",2I1,".",66I1) !A known format. WRITE (6,*) " = 11.00100100001111110110101010001000100001..." !But actually... END !So much for that.  Output: Deg. Sin(Deg) Sin(Rad) Rad - Deg ArcSinD ArcSinR Diff 0: 0.00000000 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 30: 0.50000000 0.50000000 0.00000000 30.0000000 30.0000000 0.0000000 45: 0.70710677 0.70710677 0.00000000 45.0000000 45.0000000 0.0000000 60: 0.86602539 0.86602545 0.00000006 60.0000000 60.0000038 0.0000038 90: 1.00000000 1.00000000 0.00000000 90.0000000 90.0000000 0.0000000 120: 0.86602539 0.86602539 0.00000000 60.0000000 60.0000000 0.0000000 135: 0.70710677 0.70710677 0.00000000 45.0000000 45.0000000 0.0000000 150: 0.50000000 0.50000006 0.00000006 30.0000000 30.0000038 0.0000038 180: 0.00000000 -0.00000009 -0.00000009 0.0000000 -0.0000050 -0.0000050 210: -0.50000000 -0.49999997 0.00000003 -30.0000000 -29.9999981 0.0000019 225: -0.70710677 -0.70710671 0.00000006 -45.0000000 -44.9999962 0.0000038 240: -0.86602539 -0.86602545 -0.00000006 -60.0000000 -60.0000038 -0.0000038 270: -1.00000000 -1.00000000 0.00000000 -90.0000000 -90.0000000 0.0000000 300: -0.86602539 -0.86602545 -0.00000006 -60.0000000 -60.0000038 -0.0000038 315: -0.70710677 -0.70710689 -0.00000012 -45.0000000 -45.0000076 -0.0000076 330: -0.50000000 -0.50000018 -0.00000018 -30.0000000 -30.0000114 -0.0000114 360: 0.00000000 0.00000017 0.00000017 0.0000000 0.0000100 0.0000100 Deg. Cos(Deg) Cos(Rad) Rad - Deg ArcCosD ArcCosR Diff 0: 1.00000000 1.00000000 0.00000000 0.0000000 0.0000000 0.0000000 30: 0.86602539 0.86602539 0.00000000 30.0000019 30.0000019 0.0000000 45: 0.70710677 0.70710677 0.00000000 45.0000000 45.0000000 0.0000000 60: 0.50000000 0.49999997 -0.00000003 60.0000000 60.0000038 0.0000038 90: 0.00000000 -0.00000004 -0.00000004 90.0000000 90.0000000 0.0000000 120: -0.50000000 -0.50000006 -0.00000006 120.0000000 120.0000076 0.0000076 135: -0.70710677 -0.70710677 0.00000000 135.0000000 135.0000000 0.0000000 150: -0.86602539 -0.86602539 0.00000000 150.0000000 150.0000000 0.0000000 180: -1.00000000 -1.00000000 0.00000000 180.0000000 180.0000000 0.0000000 210: -0.86602539 -0.86602539 0.00000000 150.0000000 150.0000000 0.0000000 225: -0.70710677 -0.70710683 -0.00000006 135.0000000 135.0000000 0.0000000 240: -0.50000000 -0.49999991 0.00000009 120.0000000 119.9999924 -0.0000076 270: 0.00000000 0.00000001 0.00000001 90.0000000 90.0000000 0.0000000 300: 0.50000000 0.49999991 -0.00000009 60.0000000 60.0000076 0.0000076 315: 0.70710677 0.70710665 -0.00000012 45.0000000 45.0000114 0.0000114 330: 0.86602539 0.86602533 -0.00000006 30.0000019 30.0000095 0.0000076 360: 1.00000000 1.00000000 0.00000000 0.0000000 0.0000000 0.0000000 Deg. Tan(Deg) Tan(Rad) Rad - Deg ArcTanD ArcTanR Diff 0: 0.00000000 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000 30: 0.57735026 0.57735026 0.00000000 30.0000000 30.0000000 0.0000000 45: 1.00000000 1.00000000 0.00000000 45.0000000 45.0000000 0.0000000 60: 1.73205078 1.73205090 0.00000012 60.0000000 60.0000000 0.0000000 90:************************************ 90.0000000 -90.0000000 -180.0000000 120: -1.73205078 -1.73205054 0.00000024 -60.0000000 -59.9999962 0.0000038 135: -1.00000000 -1.00000000 0.00000000 -45.0000000 -45.0000000 0.0000000 150: -0.57735026 -0.57735032 -0.00000006 -30.0000000 -30.0000019 -0.0000019 180: 0.00000000 0.00000009 0.00000009 0.0000000 0.0000050 0.0000050 210: 0.57735026 0.57735026 0.00000000 30.0000000 30.0000000 0.0000000 225: 1.00000000 0.99999988 -0.00000012 45.0000000 44.9999962 -0.0000038 240: 1.73205078 1.73205125 0.00000048 60.0000000 60.0000076 0.0000076 270:************************************ 90.0000000 -90.0000000 -180.0000000 300: -1.73205078 -1.73205113 -0.00000036 -60.0000000 -60.0000038 -0.0000038 315: -1.00000000 -1.00000024 -0.00000024 -45.0000000 -45.0000076 -0.0000076 330: -0.57735026 -0.57735056 -0.00000030 -30.0000000 -30.0000134 -0.0000134 360: 0.00000000 0.00000017 0.00000017 0.0000000 0.0000100 0.0000100 ...Special deal for 90 degrees... TanD = 1.6331778E+16 Atan = 90.00000 TanR = -2.2877332E+07 Atan = -90.00000 Pi ~ 11.00100100001111110110110000 = 11.00100100001111110110101010001000100001... Notice that the calculations in radians are less accurate. Firstly, pi cannot be represented exactly and secondly, the conversion factor of pi/180 or 180/pi adds further to the error. The degree-based functions obviously can fold their angles using exact arithmetic (though ACosD has surprising trouble with 30°) and so 360° is the same as 0°, unlike the case with radians. TanD(90°) should yield Infinity (but, which sign?) but perhaps this latter-day feature of computer floating-point was not included. In any case, Tan(90° in radians) faces the problem that its parameter will not in fact be pi/2 but some value just over (or under), and likewise with double precision and quadruple precision and any other finite precision. ## FreeBASIC {{trans|C}} ' FB 1.05.0 Win64 Const pi As Double = 4 * Atn(1) Dim As Double radians = pi / 4 Dim As Double degrees = 45.0 '' equivalent in degrees Dim As Double temp Print "Radians : "; radians, " "; Print "Degrees : "; degrees Print Print "Sine : "; Sin(radians), Sin(degrees * pi / 180) Print "Cosine : "; Cos(radians), Cos(degrees * pi / 180) Print "Tangent : "; Tan(radians), Tan(degrees * pi / 180) Print temp = ASin(Sin(radians)) Print "Arc Sine : "; temp, temp * 180 / pi temp = ACos(Cos(radians)) Print "Arc Cosine : "; temp, temp * 180 / pi temp = Atn(Tan(radians)) Print "Arc Tangent : "; temp, temp * 180 / pi Sleep  {{out}}  Radians : 0.7853981633974483 Degrees : 45 Sine : 0.7071067811865475 0.7071067811865475 Cosine : 0.7071067811865476 0.7071067811865476 Tangent : 0.9999999999999999 0.9999999999999999 Arc Sine : 0.7853981633974482 44.99999999999999 Arc Cosine : 0.7853981633974483 45 Arc Tangent : 0.7853981633974483 45  =={{header|F_Sharp|F#}}== open NUnit.Framework open FsUnit // radian [<Test>] let Verify that sin pi returns 0 () = let x = System.Math.Sin System.Math.PI System.Math.Round(x,5) |> should equal 0 [<Test>] let Verify that cos pi returns -1 () = let x = System.Math.Cos System.Math.PI System.Math.Round(x,5) |> should equal -1 [<Test>] let Verify that tan pi returns 0 () = let x = System.Math.Tan System.Math.PI System.Math.Round(x,5) |> should equal 0 [<Test>] let Verify that sin pi/2 returns 1 () = let x = System.Math.Sin (System.Math.PI / 2.0) System.Math.Round(x,5) |> should equal 1 [<Test>] let Verify that cos pi/2 returns -1 () = let x = System.Math.Cos (System.Math.PI / 2.0) System.Math.Round(x,5) |> should equal 0 [<Test>] let Verify that sin pi/3 returns sqrt 3/2 () = let actual = System.Math.Sin (System.Math.PI / 3.0) let expected = System.Math.Round((System.Math.Sqrt 3.0) / 2.0, 5) System.Math.Round(actual,5) |> should equal expected [<Test>] let Verify that cos pi/3 returns -1 () = let x = System.Math.Cos (System.Math.PI / 3.0) System.Math.Round(x,5) |> should equal 0.5 [<Test>] let Verify that cos and sin of pi/4 return same value () = let c = System.Math.Cos (System.Math.PI / 4.0) let s = System.Math.Sin (System.Math.PI / 4.0) System.Math.Round(c,5) = System.Math.Round(s,5) |> should be True [<Test>] let Verify that acos pi/3 returns 1/2 () = let actual = System.Math.Acos 0.5 let expected = System.Math.Round((System.Math.PI / 3.0),5) System.Math.Round(actual,5) |> should equal expected [<Test>] let Verify that asin 1 returns pi/2 () = let actual = System.Math.Asin 1.0 let expected = System.Math.Round((System.Math.PI / 2.0),5) System.Math.Round(actual,5) |> should equal expected [<Test>] let Verify that atan 0 returns 0 () = let actual = System.Math.Atan 0.0 let expected = System.Math.Round(0.0,5) System.Math.Round(actual,5) |> should equal expected // degree let toRadians d = d * System.Math.PI / 180.0 [<Test>] let Verify that pi is 180 degrees () = toRadians 180.0 |> should equal System.Math.PI [<Test>] let Verify that pi/2 is 90 degrees () = toRadians 90.0 |> should equal (System.Math.PI / 2.0) [<Test>] let Verify that pi/3 is 60 degrees () = toRadians 60.0 |> should equal (System.Math.PI / 3.0) [<Test>] let Verify that sin 180 returns 0 () = let x = System.Math.Sin (toRadians 180.0) System.Math.Round(x,5) |> should equal 0 [<Test>] let Verify that cos 180 returns -1 () = let x = System.Math.Cos (toRadians 180.0) System.Math.Round(x,5) |> should equal -1 [<Test>] let Verify that tan 180 returns 0 () = let x = System.Math.Tan (toRadians 180.0) System.Math.Round(x,5) |> should equal 0 [<Test>] let Verify that sin 90 returns 1 () = let x = System.Math.Sin (toRadians 90.0) System.Math.Round(x,5) |> should equal 1 [<Test>] let Verify that cos 90 returns -1 () = let x = System.Math.Cos (toRadians 90.0) System.Math.Round(x,5) |> should equal 0 [<Test>] let Verify that sin 60 returns sqrt 3/2 () = let actual = System.Math.Sin (toRadians 60.0) let expected = System.Math.Round((System.Math.Sqrt 3.0) / 2.0, 5) System.Math.Round(actual,5) |> should equal expected [<Test>] let Verify that cos 60 returns -1 () = let x = System.Math.Cos (toRadians 60.0) System.Math.Round(x,5) |> should equal 0.5 [<Test>] let Verify that cos and sin of 45 return same value () = let c = System.Math.Cos (toRadians 45.0) let s = System.Math.Sin (toRadians 45.0) System.Math.Round(c,5) = System.Math.Round(s,5) |> should be True  ## GAP # GAP has an improved floating-point support since version 4.5 Pi := Acos(-1.0); # Or use the built-in constant: Pi := FLOAT.PI; r := Pi / 5.0; d := 36; Deg := x -> x * Pi / 180; Sin(r); Asin(last); Sin(Deg(d)); Asin(last); Cos(r); Acos(last); Cos(Deg(d)); Acos(last); Tan(r); Atan(last); Tan(Deg(d)); Atan(last);  ## Go The Go math package provides the constant pi and the six trigonometric functions called for by the task. The functions all use the float64 type and work in radians. It also provides a [http://golang.org/pkg/math/#Sincos Sincos] function. package main import ( "fmt" "math" ) const d = 30. const r = d * math.Pi / 180 var s = .5 var c = math.Sqrt(3) / 2 var t = 1 / math.Sqrt(3) func main() { fmt.Printf("sin(%9.6f deg) = %f\n", d, math.Sin(d*math.Pi/180)) fmt.Printf("sin(%9.6f rad) = %f\n", r, math.Sin(r)) fmt.Printf("cos(%9.6f deg) = %f\n", d, math.Cos(d*math.Pi/180)) fmt.Printf("cos(%9.6f rad) = %f\n", r, math.Cos(r)) fmt.Printf("tan(%9.6f deg) = %f\n", d, math.Tan(d*math.Pi/180)) fmt.Printf("tan(%9.6f rad) = %f\n", r, math.Tan(r)) fmt.Printf("asin(%f) = %9.6f deg\n", s, math.Asin(s)*180/math.Pi) fmt.Printf("asin(%f) = %9.6f rad\n", s, math.Asin(s)) fmt.Printf("acos(%f) = %9.6f deg\n", c, math.Acos(c)*180/math.Pi) fmt.Printf("acos(%f) = %9.6f rad\n", c, math.Acos(c)) fmt.Printf("atan(%f) = %9.6f deg\n", t, math.Atan(t)*180/math.Pi) fmt.Printf("atan(%f) = %9.6f rad\n", t, math.Atan(t)) }  {{out}}  sin(30.000000 deg) = 0.500000 sin( 0.523599 rad) = 0.500000 cos(30.000000 deg) = 0.866025 cos( 0.523599 rad) = 0.866025 tan(30.000000 deg) = 0.577350 tan( 0.523599 rad) = 0.577350 asin(0.500000) = 30.000000 deg asin(0.500000) = 0.523599 rad acos(0.866025) = 30.000000 deg acos(0.866025) = 0.523599 rad atan(0.577350) = 30.000000 deg atan(0.577350) = 0.523599 rad  ## Groovy Trig functions use radians, degrees must be converted to/from radians def radians = Math.PI/4 def degrees = 45 def d2r = { it*Math.PI/180 } def r2d = { it*180/Math.PI } println "sin(\u03C0/4) ={Math.sin(radians)}  == sin(45\u00B0) = ${Math.sin(d2r(degrees))}" println "cos(\u03C0/4) =${Math.cos(radians)}  == cos(45\u00B0) = ${Math.cos(d2r(degrees))}" println "tan(\u03C0/4) =${Math.tan(radians)}  == tan(45\u00B0) = ${Math.tan(d2r(degrees))}" println "asin(\u221A2/2) =${Math.asin(2**(-0.5))} == asin(\u221A2/2)\u00B0 = ${r2d(Math.asin(2**(-0.5)))}\u00B0" println "acos(\u221A2/2) =${Math.acos(2**(-0.5))} == acos(\u221A2/2)\u00B0 = ${r2d(Math.acos(2**(-0.5)))}\u00B0" println "atan(1) =${Math.atan(1)} == atan(1)\u00B0 = ${r2d(Math.atan(1))}\u00B0"  {{out}} sin(π/4) = 0.7071067811865475 == sin(45°) = 0.7071067811865475 cos(π/4) = 0.7071067811865476 == cos(45°) = 0.7071067811865476 tan(π/4) = 0.9999999999999999 == tan(45°) = 0.9999999999999999 asin(√2/2) = 0.7853981633974482 == asin(√2/2)° = 44.99999999999999° acos(√2/2) = 0.7853981633974484 == acos(√2/2)° = 45.00000000000001° atan(1) = 0.7853981633974483 == atan(1)° = 45.0°  ## Haskell Trigonometric functions use radians; degrees require conversion.  a -> a fromDegrees deg = deg * pi / 180 toDegrees :: Floating a => a -> a toDegrees rad = rad * 180 / pi main :: IO () main = mapM_ print [ sin (pi / 6) , sin (fromDegrees 30) , cos (pi / 6) , cos (fromDegrees 30) , tan (pi / 6) , tan (fromDegrees 30) , asin 0.5 , toDegrees (asin 0.5) , acos 0.5 , toDegrees (acos 0.5) , atan 0.5 , toDegrees (atan 0.5) ]  {{Out}} 0.49999999999999994 0.49999999999999994 0.8660254037844387 0.8660254037844387 0.5773502691896256 0.5773502691896256 0.5235987755982988 29.999999999999996 1.0471975511965976 59.99999999999999 0.46364760900080615 26.56505117707799  ## HicEst Translated from Fortran: pi = 4.0 * ATAN(1.0) dtor = pi / 180.0 rtod = 180.0 / pi radians = pi / 4.0 degrees = 45.0 WRITE(ClipBoard) SIN(radians), SIN(degrees*dtor) WRITE(ClipBoard) COS(radians), COS(degrees*dtor) WRITE(ClipBoard) TAN(radians), TAN(degrees*dtor) WRITE(ClipBoard) ASIN(SIN(radians)), ASIN(SIN(degrees*dtor))*rtod WRITE(ClipBoard) ACOS(COS(radians)), ACOS(COS(degrees*dtor))*rtod WRITE(ClipBoard) ATAN(TAN(radians)), ATAN(TAN(degrees*dtor))*rtod  0.7071067812 0.7071067812 0.7071067812 0.7071067812 1 1 0.7853981634 45 0.7853981634 45 0.7853981634 45  SINH, COSH, TANH, and inverses are available as well. ## IDL deg = 35 ; arbitrary number of degrees rad = !dtor*deg ; system variables !dtor and !radeg convert between rad and deg  ; the trig functions receive and emit radians: print, rad, sin(rad), asin(sin(rad)) print, cos(rad), acos(cos(rad)) print, tan(rad), atan(tan(rad)) ; etc ; prints the following: ; 0.610865 0.573576 0.610865 ; 0.819152 0.610865 ; 0.700208 0.610865  ; the hyperbolic versions exist and behave as expected: print, sinh(rad) ; etc ; outputs ; 0.649572  ;If the input is an array, the output has the same dimensions etc as the input: x = !dpi/[[2,3],[4,5],[6,7]] ; !dpi is a read-only sysvar = 3.1415... print,sin(x) ;outputs: ; 1.0000000 0.86602540 ; 0.70710678 0.58778525 ; 0.50000000 0.43388374  ; the trig functions behave as expected for complex arguments: x = complex(1,2) print,sin(x) ; outputs ; ( 3.16578, 1.95960)  # == Icon and Unicon == Icon and Unicon trig functions 'sin', 'cos', 'tan', 'asin', 'acos', and 'atan' operate on angles expressed in radians. Conversion functions 'dtor' and 'rtod' convert between the two systems. The example below uses string invocation to construct and call the functions: ## Icon = invocable all procedure main() d := 30 # degrees r := dtor(d) # convert to radians every write(f := !["sin","cos","tan"],"(",r,")=",y := f(r)," ",fi := "a" || f,"(",y,")=",x := fi(y)," rad = ",rtod(x)," deg") end  {{out}} sin(0.5235987755982988)=0.4999999999999999 asin(0.4999999999999999)=0.5235987755982988 rad = 30.0 deg cos(0.5235987755982988)=0.8660254037844387 acos(0.8660254037844387)=0.5235987755982987 rad = 29.99999999999999 deg tan(0.5235987755982988)=0.5773502691896257 atan(0.5773502691896257)=0.5235987755982988 rad = 30.0 deg  = ## Unicon = The Icon solution works in Unicon. ## J The [http://www.jsoftware.com/help/dictionary/dodot.htm circle functions] in J include trigonometric functions. Native operation is in radians, so values in degrees involve conversion. Sine, cosine, and tangent of a single angle, indicated as pi-over-four radians and as 45 degrees:  (1&o. , 2&o. ,: 3&o.) (4 %~ o. 1) , 180 %~ o. 45 0.707107 0.707107 0.707107 0.707107 1 1  Arcsine, arccosine, and arctangent of one-half, in radians and degrees:  ([ ,. 180p_1&*) (_1&o. , _2&o. ,: _3&o.) 0.5 0.523599 30 1.0472 60 0.463648 26.5651  The trig script adds cover functions for the trigonometric operations as well as verbs for converting degrees from radians (dfr) and radians from degrees (rfd)  require 'trig' (sin , cos ,: tan) (1p1 % 4), rfd 45 0.707107 0.707107 0.707107 0.707107 1 1 ([ ,. dfr) (arcsin , arccos ,: arctan) 0.5 0.523599 30 1.0472 60 0.463648 26.5651  ## Java Java's Math class contains all six functions and is automatically included as part of the language. The functions all accept radians only, so conversion is necessary when dealing with degrees. The Math class also has a PI constant for easy conversion. public class Trig { public static void main(String[] args) { //Pi / 4 is 45 degrees. All answers should be the same. double radians = Math.PI / 4; double degrees = 45.0; //sine System.out.println(Math.sin(radians) + " " + Math.sin(Math.toRadians(degrees))); //cosine System.out.println(Math.cos(radians) + " " + Math.cos(Math.toRadians(degrees))); //tangent System.out.println(Math.tan(radians) + " " + Math.tan(Math.toRadians(degrees))); //arcsine double arcsin = Math.asin(Math.sin(radians)); System.out.println(arcsin + " " + Math.toDegrees(arcsin)); //arccosine double arccos = Math.acos(Math.cos(radians)); System.out.println(arccos + " " + Math.toDegrees(arccos)); //arctangent double arctan = Math.atan(Math.tan(radians)); System.out.println(arctan + " " + Math.toDegrees(arctan)); } }  {{out}}  0.7071067811865475 0.7071067811865475 0.7071067811865476 0.7071067811865476 0.9999999999999999 0.9999999999999999 0.7853981633974482 44.99999999999999 0.7853981633974483 45.0 0.7853981633974483 45.0  ## JavaScript JavaScript's Math class contains all six functions and is automatically included as part of the language. The functions all accept radians only, so conversion is necessary when dealing with degrees. The Math class also has a PI constant for easy conversion. var radians = Math.PI / 4, // Pi / 4 is 45 degrees. All answers should be the same. degrees = 45.0, sine = Math.sin(radians), cosine = Math.cos(radians), tangent = Math.tan(radians), arcsin = Math.asin(sine), arccos = Math.acos(cosine), arctan = Math.atan(tangent); // sine window.alert(sine + " " + Math.sin(degrees * Math.PI / 180)); // cosine window.alert(cosine + " " + Math.cos(degrees * Math.PI / 180)); // tangent window.alert(tangent + " " + Math.tan(degrees * Math.PI / 180)); // arcsine window.alert(arcsin + " " + (arcsin * 180 / Math.PI)); // arccosine window.alert(arccos + " " + (arccos * 180 / Math.PI)); // arctangent window.alert(arctan + " " + (arctan * 180 / Math.PI));  ## jq jq includes the standard C-library trigonometric functions (sin, cos, tan, asin, acos, atan), but they are provided as filters as illustrated in the definition of radians below. The trigonometric filters only accept radians, so conversion is necessary when dealing with degrees. The constant π can be defined as also shown in the following definition of radians:  # degrees to radians def radians: (-1|acos) as$pi | (. * $pi / 180); def task: (-1|acos) as$pi
|  ($pi / 180) as$degrees
"  sin(-pi / 6)     = $$(-pi / 6) | sin )", " cos(3 * pi / 4) = \( (3 * pi / 4) | cos)", " tan(pi / 3) = \( (pi / 3) | tan)", " asin(-1 / 2) = \((-1 / 2) | asin)", " acos(-sqrt(2)/2) = \((-(2|sqrt)/2) | acos )", " atan(sqrt(3)) = \( 3 | sqrt | atan )", "Using degrees:", " sin(-30) = \((-30 * degrees) | sin)", " cos(135) = \((135 * degrees) | cos)", " tan(60) = \(( 60 * degrees) | tan)", " asin(-1 / 2) = \( (-1 / 2) | asin / degrees)", " acos(-sqrt(2)/2) = \( (-(2|sqrt) / 2) | acos / degrees)", " atan(sqrt(3)) = \( (3 | sqrt) | atan / degrees)" ; task  {{out}} Using radians: sin(-pi / 6) = -0.49999999999999994 cos(3 * pi / 4) = -0.7071067811865475 tan(pi / 3) = 1.7320508075688767 asin(-1 / 2) = -0.5235987755982988 acos(-sqrt(2)/2) = 2.356194490192345 atan(sqrt(3)) = 1.0471975511965979 Using degrees: sin(-30) = -0.49999999999999994 cos(135) = -0.7071067811865475 tan(60) = 1.7320508075688767 asin(-1 / 2) = -29.999999999999996 acos(-sqrt(2)/2) = 135 atan(sqrt(3)) = 60.00000000000001  ## Jsish Like many programming languages that handle trig, Jsish also includes the ''atan2'' function, which was originally added to Fortran to allow disambiguous results when converting from cartesian to polar coordinates, due to the mirror image nature of normal arctan. To find what methods are supported, ''jsish'' supports help for the Math module. help Math Math.method(...) Commands performing math operations on numbers Methods: abs acos asin atan atan2 ceil cos exp floor log max min pow random round sin sqrt tan  Angles passed to the trigonometric functions expect arguments in ''radians'' (Pi by 4 radians being 45 degrees). Degree to radian conversion is shown by multiplying radians by Pi over 180. ''Note the inexact nature of floating point approximations.'' /* Trig in Jsish */ var x; ;x = Math.PI / 4; ;Math.sin(x); ;Math.cos(x); ;Math.tan(x); ;Math.asin(Math.sin(x)) * 4; ;Math.acos(Math.cos(x)) * 4; ;Math.atan(Math.tan(x)); ;Math.atan2(Math.tan(x), 1.0); ;Math.atan2(Math.tan(x), -1.0); ;x = 45.0; ;Math.sin(x * Math.PI / 180); ;Math.cos(x * Math.PI / 180); ;Math.tan(x * Math.PI / 180); /* =!EXPECTSTART!= x = Math.PI / 4 ==> 0.7853981633974483 Math.sin(x) ==> 0.7071067811865475 Math.cos(x) ==> 0.7071067811865476 Math.tan(x) ==> 0.9999999999999999 Math.asin(Math.sin(x)) * 4 ==> 3.141592653589793 Math.acos(Math.cos(x)) * 4 ==> 3.141592653589793 Math.atan(Math.tan(x)) ==> 0.7853981633974483 Math.atan2(Math.tan(x), 1.0) ==> 0.7853981633974483 Math.atan2(Math.tan(x), -1.0) ==> 2.356194490192345 x = 45.0 ==> 45 Math.sin(x * Math.PI / 180) ==> 0.7071067811865475 Math.cos(x * Math.PI / 180) ==> 0.7071067811865476 Math.tan(x * Math.PI / 180) ==> 0.9999999999999999 =!EXPECTEND!= */  {{out}} prompt jsish --U trigonometric.jsi x = Math.PI / 4 ==> 0.7853981633974483 Math.sin(x) ==> 0.7071067811865475 Math.cos(x) ==> 0.7071067811865476 Math.tan(x) ==> 0.9999999999999999 Math.asin(Math.sin(x)) * 4 ==> 3.141592653589793 Math.acos(Math.cos(x)) * 4 ==> 3.141592653589793 Math.atan(Math.tan(x)) ==> 0.7853981633974483 Math.atan2(Math.tan(x), 1.0) ==> 0.7853981633974483 Math.atan2(Math.tan(x), -1.0) ==> 2.356194490192345 x = 45.0 ==> 45 Math.sin(x * Math.PI / 180) ==> 0.7071067811865475 Math.cos(x * Math.PI / 180) ==> 0.7071067811865476 Math.tan(x * Math.PI / 180) ==> 0.9999999999999999 prompt jsish -u trigonometric.jsi [PASS] trigonometric.jsi  ## Julia # v0.6.0 rad = π / 4 deg = 45.0 @show rad deg @show sin(rad) sin(deg2rad(deg)) @show cos(rad) cos(deg2rad(deg)) @show tan(rad) tan(deg2rad(deg)) @show asin(sin(rad)) asin(sin(rad)) |> rad2deg @show acos(cos(rad)) acos(cos(rad)) |> rad2deg @show atan(tan(rad)) atan(tan(rad)) |> rad2deg  {{out}} rad = 0.7853981633974483 deg = 45.0 sin(rad) = 0.7071067811865475 sin(deg2rad(deg)) = 0.7071067811865475 cos(rad) = 0.7071067811865476 cos(deg2rad(deg)) = 0.7071067811865476 tan(rad) = 0.9999999999999999 tan(deg2rad(deg)) = 0.9999999999999999 asin(sin(rad)) = 0.7853981633974482 asin(sin(rad)) |> rad2deg = 44.99999999999999 acos(cos(rad)) = 0.7853981633974483 acos(cos(rad)) |> rad2deg = 45.0 atan(tan(rad)) = 0.7853981633974483 atan(tan(rad)) |> rad2deg = 45.0  ## Kotlin // version 1.1.2 import java.lang.Math.* fun main(args: Array<String>) { val radians = Math.PI / 4.0 val degrees = 45.0 val conv = Math.PI / 180.0 val f = "%1.15f" var inverse: Double println(" Radians Degrees") println("Angle : {f.format(radians)}\t {f.format(degrees)}\n") println("Sin : {f.format(sin(radians))}\t {f.format(sin(degrees * conv))}") println("Cos : {f.format(cos(radians))}\t {f.format(cos(degrees * conv))}") println("Tan : {f.format(tan(radians))}\t {f.format(tan(degrees * conv))}\n") inverse = asin(sin(radians)) println("ASin(Sin) : {f.format(inverse)}\t {f.format(inverse / conv)}") inverse = acos(cos(radians)) println("ACos(Cos) : {f.format(inverse)}\t {f.format(inverse / conv)}") inverse = atan(tan(radians)) println("ATan(Tan) : {f.format(inverse)}\t {f.format(inverse / conv)}") }  {{out}}  Radians Degrees Angle : 0.785398163397448 45.000000000000000 Sin : 0.707106781186548 0.707106781186548 Cos : 0.707106781186548 0.707106781186548 Tan : 1.000000000000000 1.000000000000000 ASin(Sin) : 0.785398163397448 44.999999999999990 ACos(Cos) : 0.785398163397448 45.000000000000000 ATan(Tan) : 0.785398163397448 45.000000000000000  ## Liberty BASIC pi = ACS(-1) radians = pi / 4.0 rtod = 180 / pi degrees = radians * rtod dtor = pi / 180 'LB works in radians, so degrees require conversion print "Sin: ";SIN(radians);" "; SIN(degrees*dtor) print "Cos: ";COS(radians);" "; COS(degrees*dtor) print "Tan: ";TAN(radians);" ";TAN(degrees*dtor) print "- Inverse functions:" print "Asn: ";ASN(SIN(radians));" Rad, "; ASN(SIN(degrees*dtor))*rtod;" Deg" print "Acs: ";ACS(COS(radians));" Rad, "; ACS(COS(degrees*dtor))*rtod;" Deg" print "Atn: ";ATN(TAN(radians));" Rad, "; ATN(TAN(degrees*dtor))*rtod;" Deg"  {{out}} Sin: 0.70710678 0.70710678 Cos: 0.70710678 0.70710678 Tan: 1.0 1.0 - Inverse functions: Asn: 0.78539816 Rad, 45.0 Deg Acs: 0.78539816 Rad, 45.0 Deg Atn: 0.78539816 Rad, 45.0 Deg  [[UCB Logo]] has sine, cosine, and arctangent; each having variants for degrees or radians. print sin 45 print cos 45 print arctan 1 make "pi (radarctan 0 1) * 2 ; based on quadrant if uses two parameters print radsin :pi / 4 print radcos :pi / 4 print 4 * radarctan 1  [[Lhogho]] has pi defined in its trigonometric functions. Otherwise the same as UCB Logo. print sin 45 print cos 45 print arctan 1 print radsin pi / 4 print radcos pi / 4 print 4 * radarctan 1  ## Logtalk  :- object(trignomeric_functions). :- public(show/0). show :- % standard trignomeric functions work with radians write('sin(pi/4.0) = '), SIN is sin(pi/4.0), write(SIN), nl, write('cos(pi/4.0) = '), COS is cos(pi/4.0), write(COS), nl, write('tan(pi/4.0) = '), TAN is tan(pi/4.0), write(TAN), nl, write('asin(sin(pi/4.0)) = '), ASIN is asin(sin(pi/4.0)), write(ASIN), nl, write('acos(cos(pi/4.0)) = '), ACOS is acos(cos(pi/4.0)), write(ACOS), nl, write('atan(tan(pi/4.0)) = '), ATAN is atan(tan(pi/4.0)), write(ATAN), nl, write('atan2(3,4) = '), ATAN2 is atan2(3,4), write(ATAN2), nl. :- end_object.  {{out}}  ?- trignomeric_functions::show. sin(pi/4.0) = 0.7071067811865475 cos(pi/4.0) = 0.7071067811865476 tan(pi/4.0) = 0.9999999999999999 asin(sin(pi/4.0)) = 0.7853981633974482 acos(cos(pi/4.0)) = 0.7853981633974483 atan(tan(pi/4.0)) = 0.7853981633974483 atan2(3,4) = 0.6435011087932844 yes  ## Lua print(math.cos(1), math.sin(1), math.tan(1), math.atan(1), math.atan2(3, 4))  ## Maple In radians: sin(Pi/3); cos(Pi/3); tan(Pi/3);  {{out}}  > sin(Pi/3); 1/2 3 ---- 2 > cos(Pi/3); 1/2 > tan(Pi/3); 1/2 3  The equivalent in degrees with identical output: with(Units[Standard]): sin(60*Unit(degree)); cos(60*Unit(degree)); tan(60*Unit(degree));  Note, Maple also has secant, cosecant, and cotangent: csc(Pi/3); sec(Pi/3); cot(Pi/3);  Finally, the inverse trigonometric functions: arcsin(1); arccos(1); arctan(1);  {{out}} > arcsin(1); Pi ---- 2 > arccos(1); 0 > arctan(1); Pi ---- 4  Lastly, Maple also supports the two-argument arctan plus all the hyperbolic trigonometric functions. ## Mathematica Sin[1] Cos[1] Tan[1] ArcSin[1] ArcCos[1] ArcTan[1] Sin[90 Degree] Cos[90 Degree] Tan[90 Degree]  ## MATLAB A full list of built-in trig functions can be found in the [http://www.mathworks.com/access/helpdesk/help/techdoc/ref/f16-5872.html#f16-6197 MATLAB Documentation]. function trigExample(angleDegrees) angleRadians = angleDegrees * (pi/180); disp(sprintf('sin(%f)= %f\nasin(%f)= %f',[angleRadians sin(angleRadians) sin(angleRadians) asin(sin(angleRadians))])); disp(sprintf('sind(%f)= %f\narcsind(%f)= %f',[angleDegrees sind(angleDegrees) sind(angleDegrees) asind(sind(angleDegrees))])); disp('-----------------------'); disp(sprintf('cos(%f)= %f\nacos(%f)= %f',[angleRadians cos(angleRadians) cos(angleRadians) acos(cos(angleRadians))])); disp(sprintf('cosd(%f)= %f\narccosd(%f)= %f',[angleDegrees cosd(angleDegrees) cosd(angleDegrees) acosd(cosd(angleDegrees))])); disp('-----------------------'); disp(sprintf('tan(%f)= %f\natan(%f)= %f',[angleRadians tan(angleRadians) tan(angleRadians) atan(tan(angleRadians))])); disp(sprintf('tand(%f)= %f\narctand(%f)= %f',[angleDegrees tand(angleDegrees) tand(angleDegrees) atand(tand(angleDegrees))])); end  {{out}}  trigExample(78) sin(1.361357)= 0.978148 asin(0.978148)= 1.361357 sind(78.000000)= 0.978148 arcsind(0.978148)= 78.000000 ----------------------- cos(1.361357)= 0.207912 acos(0.207912)= 1.361357 cosd(78.000000)= 0.207912 arccosd(0.207912)= 78.000000 ----------------------- tan(1.361357)= 4.704630 atan(4.704630)= 1.361357 tand(78.000000)= 4.704630 arctand(4.704630)= 78.000000  ## Maxima a: %pi / 3; [sin(a), cos(a), tan(a), sec(a), csc(a), cot(a)]; b: 1 / 2; [asin(b), acos(b), atan(b), asec(1 / b), acsc(1 / b), acot(b)]; /* Hyperbolic functions are also available */ a: 1 / 2; [sinh(a), cosh(a), tanh(a), sech(a), csch(a), coth(a)], numer; [asinh(a), acosh(1 / a), atanh(a), asech(a), acsch(a), acoth(1 / a)], numer;  ## MAXScript Maxscript trigonometric functions accept degrees only. The built-ins degToRad and radToDeg allow easy conversion. local radians = pi / 4 local degrees = 45.0 --sine print (sin (radToDeg radians)) print (sin degrees) --cosine print (cos (radToDeg radians)) print (cos degrees) --tangent print (tan (radToDeg radians)) print (tan degrees) --arcsine print (asin (sin (radToDeg radians))) print (asin (sin degrees)) --arccosine print (acos (cos (radToDeg radians))) print (acos (cos degrees)) --arctangent print (atan (tan (radToDeg radians))) print (atan (tan degrees))  ## Metafont Metafont has sind and cosd, which compute sine and cosine of an angle expressed in degree. We need to define the rest. Pi := 3.14159; vardef torad expr x = Pi*x/180 enddef; % conversions vardef todeg expr x = 180x/Pi enddef; vardef sin expr x = sind(todeg(x)) enddef; % radians version of sind vardef cos expr x = cosd(todeg(x)) enddef; % and cosd vardef sign expr x = if x>=0: 1 else: -1 fi enddef; % commodity vardef tand expr x = % tan with arg in degree if cosd(x) = 0: infinity * sign(sind(x)) else: sind(x)/cosd(x) fi enddef; vardef tan expr x = tand(todeg(x)) enddef; % arg in rad % INVERSE % the arc having x as tanget is that between x-axis and a line % from the center to the point (1, x); MF angle says this vardef atand expr x = angle(1,x) enddef; vardef atan expr x = torad(atand(x)) enddef; % rad version % known formula to express asin and acos in function of % atan; a+-+b stays for sqrt(a^2 - b^2) (defined in plain MF) vardef asin expr x = 2atan(x/(1+(1+-+x))) enddef; vardef acos expr x = 2atan((1+-+x)/(1+x)) enddef; vardef asind expr x = todeg(asin(x)) enddef; % degree versions vardef acosd expr x = todeg(acos(x)) enddef; % commodity def outcompare(expr a, b) = message decimal a & " = " & decimal b enddef; % output tests outcompare(torad(60), Pi/3); outcompare(todeg(Pi/6), 30); outcompare(Pi/3, asin(sind(60))); outcompare(30, acosd(cos(Pi/6))); outcompare(45, atand(tand(45))); outcompare(Pi/4, atan(tand(45))); outcompare(sin(Pi/3), sind(60)); outcompare(cos(Pi/4), cosd(45)); outcompare(tan(Pi/3), tand(60)); end  ## MiniScript pi3 = pi/3 degToRad = pi/180 print "sin PI/3 radians = " + sin(pi3) print "sin 60 degrees = " + sin(60*degToRad) print "arcsin 0.5 in radians = " + asin(0.5) print "arcsin 0.5 in degrees = " + asin(0.5)/degToRad print "cos PI/3 radians = " + cos(pi3) print "cos 60 degrees = " + cos(60*degToRad) print "arccos 0.5 in radians = " + acos(0.5) print "arccos 0.5 in degrees = " + acos(0.5)/degToRad print "tan PI/3 radians = " + tan(pi3) print "tan 60 degrees = " + tan(60*degToRad) print "arctan 0.5 in radians = " + atan(0.5) print "arctan 0.5 in degrees = " + atan(0.5)/degToRad  {{out}}  sin PI/3 radians = 0.866025 sin 60 degrees = 0.866025 arcsin 0.5 in radians = 0.523599 arcsin 0.5 in degrees = 30.0 cos PI/3 radians = 0.5 cos 60 degrees = 0.5 arccos 0.5 in radians = 1.047198 arccos 0.5 in degrees = 60.0 tan PI/3 radians = 1.732051 tan 60 degrees = 1.732051 arctan 0.5 in radians = 0.463648 arctan 0.5 in degrees = 26.565051  =={{header|МК-61/52}}==  sin С/П Вx cos С/П Вx tg С/П Вx arcsin С/П Вx arccos С/П Вx arctg С/П  Setting the units of angle (degrees, radians, grads) takes care of the switch ''Р-ГРД-Г''. =={{header|Modula-2}}== MODULE Trig; FROM RealMath IMPORT pi,sin,cos,tan,arctan,arccos,arcsin; FROM RealStr IMPORT RealToStr; FROM Terminal IMPORT WriteString,WriteLn,ReadChar; PROCEDURE WriteReal(v : REAL); VAR buf : ARRAY[0..31] OF CHAR; BEGIN RealToStr(v, buf); WriteString(buf) END WriteReal; VAR theta : REAL; BEGIN theta := pi / 4.0; WriteString("theta: "); WriteReal(theta); WriteLn; WriteString("sin: "); WriteReal(sin(theta)); WriteLn; WriteString("cos: "); WriteReal(cos(theta)); WriteLn; WriteString("tan: "); WriteReal(tan(theta)); WriteLn; WriteString("arcsin: "); WriteReal(arcsin(sin(theta))); WriteLn; WriteString("arccos: "); WriteReal(arccos(cos(theta))); WriteLn; WriteString("arctan: "); WriteReal(arctan(tan(theta))); WriteLn; ReadChar END Trig.  ## NetRexx /* NetRexx */ options replace format comments java crossref symbols nobinary utf8 numeric digits 30 parse 'Radians Degrees angle' RADIANS DEGREES ANGLE .; parse 'sine cosine tangent arcsine arccosine arctangent' SINE COSINE TANGENT ARCSINE ARCCOSINE ARCTANGENT . trigVals = '' trigVals[RADIANS, ANGLE ] = (Rexx Math.PI) / 4 -- Pi/4 == 45 degrees trigVals[DEGREES, ANGLE ] = 45.0 trigVals[RADIANS, SINE ] = (Rexx Math.sin(trigVals[RADIANS, ANGLE])) trigVals[DEGREES, SINE ] = (Rexx Math.sin(Math.toRadians(trigVals[DEGREES, ANGLE]))) trigVals[RADIANS, COSINE ] = (Rexx Math.cos(trigVals[RADIANS, ANGLE])) trigVals[DEGREES, COSINE ] = (Rexx Math.cos(Math.toRadians(trigVals[DEGREES, ANGLE]))) trigVals[RADIANS, TANGENT ] = (Rexx Math.tan(trigVals[RADIANS, ANGLE])) trigVals[DEGREES, TANGENT ] = (Rexx Math.tan(Math.toRadians(trigVals[DEGREES, ANGLE]))) trigVals[RADIANS, ARCSINE ] = (Rexx Math.asin(trigVals[RADIANS, SINE])) trigVals[DEGREES, ARCSINE ] = (Rexx Math.toDegrees(Math.acos(trigVals[DEGREES, SINE]))) trigVals[RADIANS, ARCCOSINE ] = (Rexx Math.acos(trigVals[RADIANS, COSINE])) trigVals[DEGREES, ARCCOSINE ] = (Rexx Math.toDegrees(Math.acos(trigVals[DEGREES, COSINE]))) trigVals[RADIANS, ARCTANGENT] = (Rexx Math.atan(trigVals[RADIANS, TANGENT])) trigVals[DEGREES, ARCTANGENT] = (Rexx Math.toDegrees(Math.atan(trigVals[DEGREES, TANGENT]))) say ' '.right(12)'|' RADIANS.right(17) '|' DEGREES.right(17) '|' say ANGLE.right(12)'|' trigVals[RADIANS, ANGLE ].format(4, 12) '|' trigVals[DEGREES, ANGLE ].format(4, 12) '|' say SINE.right(12)'|' trigVals[RADIANS, SINE ].format(4, 12) '|' trigVals[DEGREES, SINE ].format(4, 12) '|' say COSINE.right(12)'|' trigVals[RADIANS, COSINE ].format(4, 12) '|' trigVals[DEGREES, COSINE ].format(4, 12) '|' say TANGENT.right(12)'|' trigVals[RADIANS, TANGENT ].format(4, 12) '|' trigVals[DEGREES, TANGENT ].format(4, 12) '|' say ARCSINE.right(12)'|' trigVals[RADIANS, ARCSINE ].format(4, 12) '|' trigVals[DEGREES, ARCSINE ].format(4, 12) '|' say ARCCOSINE.right(12)'|' trigVals[RADIANS, ARCCOSINE ].format(4, 12) '|' trigVals[DEGREES, ARCCOSINE ].format(4, 12) '|' say ARCTANGENT.right(12)'|' trigVals[RADIANS, ARCTANGENT].format(4, 12) '|' trigVals[DEGREES, ARCTANGENT].format(4, 12) '|' say return  {{out}}  | Radians | Degrees | angle| 0.785398163397 | 45.000000000000 | sine| 0.707106781187 | 0.707106781187 | cosine| 0.707106781187 | 0.707106781187 | tangent| 1.000000000000 | 1.000000000000 | arcsine| 0.785398163397 | 45.000000000000 | arccosine| 0.785398163397 | 45.000000000000 | arctangent| 0.785398163397 | 45.000000000000 |  ## Nim import math proc radians(x): float = x * Pi / 180 proc degrees(x): float = x * 180 / Pi let rad = Pi/4 let deg = 45.0 echo "Sine: ", sin(rad), " ", sin(radians(deg)) echo "Cosine : ", cos(rad), " ", cos(radians(deg)) echo "Tangent: ", tan(rad), " ", tan(radians(deg)) echo "Arcsine: ", arcsin(sin(rad)), " ", degrees(arcsin(sin(radians(deg)))) echo "Arccocose: ", arccos(cos(rad)), " ", degrees(arccos(cos(radians(deg)))) echo "Arctangent: ", arctan(tan(rad)), " ", degrees(arctan(tan(radians(deg))))  ## OCaml OCaml's preloaded Pervasives module contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees. let pi = 4. *. atan 1. let radians = pi /. 4. let degrees = 45.;; Printf.printf "%f %f\n" (sin radians) (sin (degrees *. pi /. 180.));; Printf.printf "%f %f\n" (cos radians) (cos (degrees *. pi /. 180.));; Printf.printf "%f %f\n" (tan radians) (tan (degrees *. pi /. 180.));; let arcsin = asin (sin radians);; Printf.printf "%f %f\n" arcsin (arcsin *. 180. /. pi);; let arccos = acos (cos radians);; Printf.printf "%f %f\n" arccos (arccos *. 180. /. pi);; let arctan = atan (tan radians);; Printf.printf "%f %f\n" arctan (arctan *. 180. /. pi);;  {{out}}  0.707107 0.707107 0.707107 0.707107 1.000000 1.000000 0.785398 45.000000 0.785398 45.000000 0.785398 45.000000  ## Octave function d = degree(rad) d = 180*rad/pi; endfunction r = pi/3; rd = degree(r); funcs = { "sin", "cos", "tan", "sec", "cot", "csc" }; ifuncs = { "asin", "acos", "atan", "asec", "acot", "acsc" }; for i = 1 : numel(funcs) v = arrayfun(funcs{i}, r); vd = arrayfun(strcat(funcs{i}, "d"), rd); iv = arrayfun(ifuncs{i}, v); ivd = arrayfun(strcat(ifuncs{i}, "d"), vd); printf("%s(%f) = %s(%f) = %f (%f)\n", funcs{i}, r, strcat(funcs{i}, "d"), rd, v, vd); printf("%s(%f) = %f\n%s(%f) = %f\n", ifuncs{i}, v, iv, strcat(ifuncs{i}, "d"), vd, ivd); endfor  {{out}} sin(1.047198) = sind(60.000000) = 0.866025 (0.866025) asin(0.866025) = 1.047198 asind(0.866025) = 60.000000 cos(1.047198) = cosd(60.000000) = 0.500000 (0.500000) acos(0.500000) = 1.047198 acosd(0.500000) = 60.000000 tan(1.047198) = tand(60.000000) = 1.732051 (1.732051) atan(1.732051) = 1.047198 atand(1.732051) = 60.000000 sec(1.047198) = secd(60.000000) = 2.000000 (2.000000) asec(2.000000) = 1.047198 asecd(2.000000) = 60.000000 cot(1.047198) = cotd(60.000000) = 0.577350 (0.577350) acot(0.577350) = 1.047198 acotd(0.577350) = 60.000000 csc(1.047198) = cscd(60.000000) = 1.154701 (1.154701) acsc(1.154701) = 1.047198 acscd(1.154701) = 60.000000  (Lacking in this code but present in GNU Octave: sinh, cosh, tanh, coth and inverses) ## Oforth import: math : testTrigo | rad deg hyp z | Pi 4 / ->rad 45.0 ->deg 0.5 ->hyp System.Out rad sin << " - " << deg asRadian sin << cr System.Out rad cos << " - " << deg asRadian cos << cr System.Out rad tan << " - " << deg asRadian tan << cr printcr rad sin asin ->z System.Out z << " - " << z asDegree << cr rad cos acos ->z System.Out z << " - " << z asDegree << cr rad tan atan ->z System.Out z << " - " << z asDegree << cr printcr System.Out hyp sinh << " - " << hyp sinh asinh << cr System.Out hyp cosh << " - " << hyp cosh acosh << cr System.Out hyp tanh << " - " << hyp tanh atanh << cr ;  {{out}}  0.707106781186547 - 0.707106781186547 0.707106781186548 - 0.707106781186548 1 - 1 0.785398163397448 - 45 0.785398163397448 - 45 0.785398163397448 - 45 0.521095305493747 - 0.5 1.12762596520638 - 0.5 0.46211715726001 - 0.5  ## ooRexx  rxm.cls 20 March 2014 The distribution of ooRexx contains a function package called rxMath that provides the computation of trigonometric and some other functions. Based on the underlying C-library the precision of the returned values is limited to 16 digits. Close observation show that sometimes the last one to three digits of the returned values are not correct. Many years ago I experimented with implementing these functions in Rexx with its virtually unlimited precision. The rxm class is intended to provide the same functionality as rxMath with no limit on the specified or implied precision. Functions in class rxm and invocation syntax are the same as in the rxMath library. They are implemented as routines which perform the checking of argument values and invoke the corresponding methods. Here is a list of the supported functions and a concise syntax specification. The arguments are represented by these letters: x is the value for which the respective function must be evaluated. b and c for RxCalcPower are base and exponent, respectively. p if specified is the desired precision (number of digits) in the result. It can be any integer from 1 to 999999. See below for the default used. u if specified, is the unit of x given to the trigonometric functions or the unit of the value returned by the Arcus functions. It can be 'R', 'D', or 'G' for radians, degrees, or grades, respectively. See below for the default used. Trigonometric functions: • rxmCos(x[,[p][,u]]) • rxmCotan(x[,[p][,u]]) • rxmSin(x[,[p][,u]]) • rxmTan(x[,[p][,u]]) Arcus functions: • rxmArcCos(x[,[p][,u]]) • rxmArcSin(x[,[p][,u]]) • rxmArcTan(x[,[p][,u]]) Hyperbolic functions: • rxmCosH(x[,p]) • rxmSinH(x[,p]) • rxmTanH(x[,p]) • rxmExp(x[,p]) e**x • rxmLog(x[,p]) Natural logarithm of x • rxmLog10(x[,p]) Brigg's logarithm of x • rxmSqrt(x[,p]) Square root of x • rxmPower(b,c[,p]) b**c • rxmPi([p]) pi to the specified or default precision Values used for p and u if these are omitted in the invocation ### ======================================================== The directive ::REQUIRES rxm.cls creates an instance of the class .local~my.rxm=.rxm~new(16,"D") which sets the defaults for p=16 and u='D'. These are used when p or u are omitted in a function invocation. They can be changed by changing the respective class attributes as follows: .locaL~my.rxm~precision=50 .locaL~my.rxm~type='R' The current setting of these attributes can be retrieved as follows: .locaL~my.rxm~precision() .locaL~my.rxm~type() While I tried to get full compatibility there remain a few (actually very few) differences: rxCalcTan(90) raises the Syntax condition (will be fixed in the next ooRexx release) rxCalcexp(x) limits x to 709. or so and returns '+infinity' for larger exponents  /* REXX --------------------------------------------------------------- * show how the functions can be used * 03.05.2014 Walter Pachl *--------------------------------------------------------------------*/ Say 'Default precision:' .locaL~my.rxm~precision() Say 'Default type: ' .locaL~my.rxm~type() Say 'rxmsin(60) ='rxmsin(60) -- use default precision and type Say 'rxmsin(1,21,"R")='rxmsin(1,21,'R') -- precision and type specified Say 'rxmlog(-1) ='rxmlog(-1) Say 'rxmlog( 0) ='rxmlog( 0) Say 'rxmlog( 1) ='rxmlog( 1) Say 'rxmlog( 2) ='rxmlog( 2) .locaL~my.rxm~precision=50 .locaL~my.rxm~type='R' Say 'Changed precision:' .locaL~my.rxm~precision() Say 'Changed type: ' .locaL~my.rxm~type() Say 'rxmsin(1) ='rxmsin(1) -- use changed precision and type ::requires rxm.cls  {{out}} Default precision: 16 Default type: D rxmsin(60) =0.8660254037844386 rxmsin(1,21,"R")=0.841470984807896506653 rxmlog(-1) =nan rxmlog( 0) =-infinity rxmlog( 1) =0 rxmlog( 2) =0.6931471805599453 Changed precision: 50 Changed type: R rxmsin(1) =0.84147098480789650665250232163029899962256306079837  /******************************************************************** * Package rxm * implements the functions available in RxMath with high precision * by computing the values with significantly increased precision * and rounding the result to the specified precision. * This started 10 years ago when Vladimir Zabrodsky published his * Album of Algorithms http://dhost.info/zabrodskyvlada/aat/ * Gerard Schildberger suggests on rosettacode.org to use +10 digits * Rony Flatscher suggested and helped to turn this into an ooRexx class * Rick McGuire advised on using Use STRICT Arg for argument checking * Alexander Seik creates this documentation * Horst Wegscheider helped with reviewing and some improvements * 12.04.2014 Walter Pachl * Documentation: see rxmath.pdf in the ooRexx distribution * and rxm.doc (here) * 13.04.2014 WP arcsin and arctan commentary corrected (courtesy Horst) * 13.04.2014 WP improve arctan performance * 20.04.2014 WP towards completion * 24.04.2014 WP arcsin verbessert. courtesy Horst Wegscheider * 28.04.2014 WP run ooRexxDoc * 11.08.2014 WP replace log algorithm with Vladimir Zabrodsky's code **********************************************************************/ .local~my.rxm=.rxm~new(16,"D") ::Class rxm Public ::Method init Expose precision type Use Arg precision=(digits()),type='D' ::attribute precision set Expose precision Use Strict Arg precision=(digits()) ::attribute precision get ::attribute type set Expose type Use Strict Arg type='R' ::attribute type get ::Method arccos /*********************************************************************** * Return arccos(x,precision,type) -- with specified precision * arccos(x) = pi/2 - arcsin(x) ***********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 Numeric Digits iprec If x=1 Then r=0 Else Do r=self~arcsin(x,iprec,'R') If r='nan' Then Return r r=self~pi(iprec)/2 - r End Select When xtype='D' Then r=r*180/self~pi(iprec) When xtype='G' Then r=r*200/self~pi(iprec) Otherwise Nop End Numeric Digits xprec Return (r+0) ::Method arcsin /*********************************************************************** * Return arcsin(x,precision,type) -- with specified precision * arcsin(x) = x+(x**3)*1/2*3+(x**5)*1*3/2*4*5+(x**7)*1*3*5/2*4*6*7+... ***********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 Numeric Digits iprec sign=sign(x) If x<0 Then x=abs(x) Select When abs(x)>1 Then Return 'nan' When x=0 Then r=0 When x=1 Then r=rxmpi(iprec)/2 When x<0.8 Then Do o=x u=1 r=x Do i=3 By 2 Until ra=r ra=r o=o*x*x*(i-2) u=u*(i-1)*i/(i-2) r=r+(o/u) If r=ra Then r=r+(o/u)/2 /* final touch */ End End Otherwise Do z=x r=x o=x s=x*x do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=r then leave r=z; end /*********************** y=(1-x*x)/4 n=0.5-self~sqrt(y,iprec) z=self~sqrt(n,iprec) r=2*self~arcsin(z,xprec) ***********************/ End End Select When xtype='D' Then r=r*180/self~pi(iprec) When xtype='G' Then r=r*200/self~pi(iprec) Otherwise Nop End Numeric Digits xprec Return sign*(r+0) ::Method arctan /*********************************************************************** * Return arctan(x,precision,type) -- with specified precision * x=0 -> arctan(x) = 0 * If x>0 Then * x<1 -> arctan(x) = arcsin(x/sqrt(x**2+1)) * x=1 -> arctan(x) = pi/4 * x>1 -> arctan(x) = pi/2-arcsin((1/x)/sqrt((1/x)**2+1)) * Else * adjust as necessary ***********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 Numeric Digits iprec Select When abs(x)<1 Then r=self~arcsin(x/self~sqrt(1+x**2,iprec),iprec,'R') When abs(x)=1 Then r=self~pi(iprec)/4*sign(x) Otherwise Do xr=1/abs(x) r=self~arcsin(xr/self~sqrt(1+xr**2,iprec),iprec,'R') If x>0 Then r=self~pi(iprec)/2-r Else r=-self~pi(iprec)/2+r End End Select When xtype='D' Then r=r*180/self~pi(iprec) When xtype='G' Then r=r*200/self~pi(iprec) Otherwise Nop End Numeric Digits xprec Return (r+0) ::Method arsinh /*********************************************************************** * Return arsinh(x,precision,type) -- with specified precision * arsinh(x) = ln(x+sqrt(x**2+1)) ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision) iprec=xprec+10 Numeric Digits iprec x2p1=x**2+1 r=self~log(x+self~sqrt(x2p1,iprec),iprec) Numeric Digits xprec Return (r+0) ::Method cos /* REXX ************************************************************* * Return cos(x,precision,type) -- with the specified precision * cos(x)=sin(x+pi/2) ********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 Numeric Digits iprec Select When xtype='R' Then xa=x+self~pi(iprec)/2 When xtype='D' Then xa=x+90 When xtype='G' Then xa=x+100 End r=self~sin(xa,iprec,xtype) Numeric Digits xprec Return (r+0) ::Method cosh /* REXX **************************************************************** * Return cosh(x,precision,type) -- with specified precision * cosh(x) = 1+(x**2/2!)+(x**4/4!)+(x**6/6!)+-... ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision) iprec=xprec+10 Numeric Digits iprec o=1 u=1 r=1 Do i=2 By 2 Until ra=r ra=r o=o*x*x u=u*i*(i-1) r=r+(o/u) End Numeric Digits xprec Return (r+0) ::Method cotan /* REXX ************************************************************* * Return cotan(x,precision,type) -- with the specified precision * cot(x)=cos(x)/sin(x) ********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 Numeric Digits iprec s=self~sin(x,iprec,xtype) c=self~cos(x,iprec,xtype) If s=0 Then Return '+infinity' r=c/s Numeric Digits xprec Return (r+0) ::Method exp /*********************************************************************** * exp(x,precision) returns e**x -- with specified precision * exp(x,precision,base) returns base**x -- with specified precision ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision),xbase='' iprec=xprec+10 Numeric Digits iprec Numeric Fuzz 3 If xbase<>'' Then Do Select When xbase=0 Then Do Select When x<0 Then Return '+infinity' When x=0 Then Return 'nan' Otherwise Return 0 End End When xbase=1 Then Return 1 When xbase<0 Then Do Select When x=0 Then Return 1 When datatype(x,'W')=0 Then Return 'nan' Otherwise Do r=xbase**x Numeric Digits xprec Return r+0 End End End Otherwise x=x*self~log(xbase,iprec) End End o=1 u=1 r=1 Do i=1 By 1 Until ra=r ra=r o=o*x u=u*i r=r+(o/u) End Numeric Digits xprec Return (r+0) ::Method log /*********************************************************************** * log(x,precision) -- returns ln(x) with specified precision * log(x,precision,base) -- returns blog(x) with specified precision * Three different series are used for ln(x): x in range 0 to 0.5 * 0.5 to 1.5 * 1.5 to infinity ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision),xbase='' iprec=xprec+100 Numeric Digits iprec Select When x=0 Then Return '-infinity' When x<0 Then Return 'nan' When x<1 Then r= -self~Log(1/X,xprec) Otherwise Do do M = 0 until (2 ** M) > X; end M = M - 1 Z = X / (2 ** M) Zeta = (1 - Z) / (1 + Z) N = Zeta; Ln = Zeta; Zetasup2 = Zeta * Zeta do J = 1 N = N * Zetasup2; NewLn = Ln + N / (2 * J + 1) if NewLn = Ln then Do r= M * self~LN2P(xprec) - 2 * Ln Leave End Ln = NewLn end End End If x>0 Then Do If xbase>'' Then r=r/self~log(xbase,iprec) Numeric Digits xprec r=r+0 End Return r ::Method ln2p Parse Arg p Numeric Digits p+10 If p<=1000 Then Return self~ln2() n=1/3 ln=n zetasup2=1/9 Do j=1 n=n*zetasup2 newln=ln+n/(2*j+1) If newln=ln Then Return 2*ln ln=newln End ::Method LN2 V = '' V = V || 0.69314718055994530941723212145817656807 V = V || 5500134360255254120680009493393621969694 V = V || 7156058633269964186875420014810205706857 V = V || 3368552023575813055703267075163507596193 V = V || 0727570828371435190307038623891673471123350 v='' v=v||0.69314718055994530941723212145817656807 v=v||5500134360255254120680009493393621969694 v=v||7156058633269964186875420014810205706857 v=v||3368552023575813055703267075163507596193 v=v||0727570828371435190307038623891673471123 v=v||3501153644979552391204751726815749320651 v=v||5552473413952588295045300709532636664265 v=v||4104239157814952043740430385500801944170 v=v||6416715186447128399681717845469570262716 v=v||3106454615025720740248163777338963855069 v=v||5260668341137273873722928956493547025762 v=v||6520988596932019650585547647033067936544 v=v||3254763274495125040606943814710468994650 v=v||6220167720424524529612687946546193165174 v=v||6813926725041038025462596568691441928716 v=v||0829380317271436778265487756648508567407 v=v||7648451464439940461422603193096735402574 v=v||4460703080960850474866385231381816767514 v=v||3866747664789088143714198549423151997354 v=v||8803751658612753529166100071053558249879 v=v||4147295092931138971559982056543928717000 v=v||7218085761025236889213244971389320378439 v=v||3530887748259701715591070882368362758984 v=v||2589185353024363421436706118923678919237 v=v||231467232172053401649256872747782344535348 return V ::Method log10 /*********************************************************************** * Return log10(x,prec) specified precision ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision) iprec=xprec+10 r=self~log(x,iprec,10) Numeric Digits xprec Return (r+0) ::Method pi /* REXX ************************************************************* * Return pi with the specified precision ********************************************************************/ Expose precision Use Strict Arg xprec=(precision) p='3.141592653589793238462643383279502884197169399375'||, '10582097494459230781640628620899862803482534211706'||, '79821480865132823066470938446095505822317253594081'||, '28481117450284102701938521105559644622948954930381'||, '96442881097566593344612847564823378678316527120190'||, '91456485669234603486104543266482133936072602491412'||, '73724587006606315588174881520920962829254091715364'||, '36789259036001133053054882046652138414695194151160'||, '94330572703657595919530921861173819326117931051185'||, '48074462379962749567351885752724891227938183011949'||, '12983367336244065664308602139494639522473719070217'||, '98609437027705392171762931767523846748184676694051'||, '32000568127145263560827785771342757789609173637178'||, '72146844090122495343014654958537105079227968925892'||, '35420199561121290219608640344181598136297747713099'||, '60518707211349999998372978049951059731732816096318'||, '59502445945534690830264252230825334468503526193118'||, '81710100031378387528865875332083814206171776691473'||, '03598253490428755468731159562863882353787593751957'||, '781857780532171226806613001927876611195909216420199' If xprec>1000 Then Do /* more than 1000 digits wanted */ iprec=xprec+10 /* internal precision */ Numeric Digits iprec new=1 a=sqrt(2,iprec) b=0 p=2+a Do i=1 By 1 Until p=pi pi=p y=self~sqrt(a,iprec) a1=(y+1/y)/2 b1=y*(b+1)/(b+a) p=pi*b1*(1+a1)/(1+b1) a=a1 b=b1 End End Numeric Digits xprec Return (p+0) ::Method power /*********************************************************************** * power(base,exponent,precision) returns base**exponent * -- with specified precision ***********************************************************************/ Expose precision Use Strict Arg b,c,xprec=(precision) Numeric Digits xprec rsign=1 If b<0 Then Do /* negative base */ If datatype(c,'W') Then Do /* Exponent is an integer */ If c//2=1 Then /* .. an odd number */ rsign=-1 /* Resuld will be negative */ b=abs(b) /* proceed with positive base */ End Else Do /* Exponent is not an integer */ -- Say 'for a negative base ('||b')', 'exponent ('c') must be an integer' Return 'nan' /* Return not a number */ End End If c=0 Then Do If b>=0 Then r=1 End Else r=self~exp(c,xprec,b) If datatype(r)<>'NUM' Then Return r Return rsign*r ::Method sqrt /* REXX ************************************************************* * Return sqrt(x,precision) -- with the specified precision ********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision) If x<0 Then Do Return 'nan' End iprec=xprec+10 Numeric Digits iprec r0= x r = 1 Do i=1 By 1 Until r=r0 | (abs(r*r-x)<10**-iprec) r0 = r r = (r + x/r) / 2 End Numeric Digits xprec Return (r+0) ::Method sin /* REXX ************************************************************* * Return sin(x,precision,type) -- with the specified precision * xtype = 'R' (radians, default) 'D' (degrees) 'G' (grades) * sin(x) = x-(x**3/3!)+(x**5/5!)-(x**7/7!)+-... ********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 /* internal precision */ Numeric Digits iprec /* first use pi constant or compute it if necessary */ pi=self~pi(iprec) /* normalize x to be between 0 and 2*pi (or equivalent) */ /* and convert degrees or grades to radians */ xx=x Select When xtype='R' Then Do Do While xx>=pi*2; xx=xx-pi*2; End Do While xx<0; xx=xx+pi*2; End End When xtype='D' Then Do Do While xx>=360; xx=xx-360; End Do While xx<0; xx=xx+360; End xx=xx*pi/180 End When xtype='G' Then Do Do While xx>=400; xx=xx-400; End Do While xx<0; xx=xx+400; End xx=xx*pi/200 End End /* normalize xx to be between 0 and pi/2 */ sign=1 Select When xx<=pi/2 Then Nop When xx<=pi Then xx=pi-xx When xx<=3*pi/2 Then Do; sign=-1; xx=xx-pi; End Otherwise Do; sign=-1; xx=2*pi-xx; End End /* now compute the Taylor series for the normalized xx */ o=xx u=1 r=xx If abs(xx)<10**(-iprec) Then r=0 Else Do Do i=3 By 2 Until ra=r ra=r o=-o*xx*xx u=u*i*(i-1) r=r+(o/u) End End Numeric Digits xprec Return sign*(r+0) ::Method sinh /* REXX **************************************************************** * Return sinh(x,precision) -- with specified precision * sinh(x) = x+(x**3/3!)+(x**5/5!)+(x**7/7!)+-... * 920903 Walter Pachl ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision) iprec=xprec+10 Numeric Digits iprec o=x u=1 r=x Do i=3 By 2 Until ra=r ra=r o=o*x*x u=u*i*(i-1) r=r+(o/u) End Numeric Digits xprec Return (r+0) ::Method tan /* REXX ************************************************************* * Return tan(x,precision,type) -- with the specified precision * tan(x)=sin(x)/cos(x) ********************************************************************/ Expose precision type Use Strict Arg x,xprec=(precision),xtype=(type) iprec=xprec+10 Numeric Digits iprec s=self~sin(x,iprec,xtype) c=self~cos(x,iprec,xtype) If c=0 Then Return '+infinity' t=s/c Numeric Digits xprec Return (t+0) ::Method tanh /*********************************************************************** * Return tanh(x,precision) -- with specified precision * tanh(x) = sinh(x)/cosh(x) ***********************************************************************/ Expose precision Use Strict Arg x,xprec=(precision) iprec=xprec+10 Numeric Digits iprec r=self~sinh(x,iprec)/self~cosh(x,iprec) Numeric Digits xprec Return (r+0) ::routine rxmarccos public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If x<-1 | 1<x Then Return 'nan' return .my.rxm~arccos(x,xprec,xtype) ::routine rxmarcsin public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If wordpos(xtype,'R D G')=0 Then Do -- Say 'Argument 3 must be R, D, or G' Raise Syntax 88.907 array(3,'R, D, or G',xtype) End If x<-1 | 1<x Then Return 'nan' return .my.rxm~arcsin(x,xprec,xtype) ::routine rxmarctan public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If wordpos(xtype,'R D G')=0 Then Do -- Say 'Argument 3 must be R, D, or G' Raise Syntax 88.907 array(3,'R, D, or G',xtype) End return .my.rxm~arctan(x,xprec,xtype) ::routine rxmarsinh public Use Strict Arg x,xprec=(.my.rxm~precision) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End return .my.rxm~arsinh(x,xprec) ::routine rxmcos public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If wordpos(xtype,'R D G')=0 Then Do -- Say 'Argument 3 must be R, D, or G' Raise Syntax 88.907 array(3,'R, D, or G',xtype) End return .my.rxm~cos(x,xprec,xtype) ::routine rxmcosh public Use Strict Arg x,xprec=(.my.rxm~precision) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End return .my.rxm~cosh(x,xprec) ::routine rxmcotan public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If wordpos(xtype,'R D G')=0 Then Do -- Say 'Argument 3 must be R, D, or G' Raise Syntax 88.907 array(3,'R, D, or G',xtype) End return .my.rxm~cotan(x,xprec) ::routine rxmexp public Use Strict Arg x,xprec=(.my.rxm~precision),xbase='' If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If datatype(xbase,'NUM')=0 & xbase<>'' Then Do -- Say 'Argument 3 must be omitted or a number' Raise Syntax 88.902 array(3,xbase) End Select When x<0 Then Do iprec=xprec+10 Numeric Digits iprec z=.my.rxm~exp(abs(x),iprec,xbase) Select When z=0 Then Return '+infinity' When datatype(z)<>'NUM' Then Return z Otherwise r=1/z End Numeric Digits xprec return r+0 End When x=0 Then Do If xbase=0 Then Return 'nan' Else Return 1 End Otherwise return .my.rxm~exp(x,xprec,xbase) End ::routine rxmlog public Use Strict Arg x,xprec=(.my.rxm~precision),xbase='' If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If xbase<>'' &, datatype(xbase,'NUM')=0 Then Do -- Say 'Argument 3 must be a number' Raise Syntax 88.902 array(3,xbase) End If x=0 Then Return '-infinity' If x<0 Then Return 'nan' return .my.rxm~log(x,xprec,xbase) ::routine rxmlog10 public Use Strict Arg x,xprec=(.my.rxm~precision) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If x=0 Then Return '-infinity' If x<0 Then Return 'nan' return .my.rxm~log10(x,xprec) ::routine rxmpi public Use Strict Arg xprec=(.my.rxm~precision) If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End return .my.rxm~pi(xprec) ::routine rxmpower public Use Strict Arg b,e,xprec=(.my.rxm~precision) If datatype(b,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,b) End If datatype(e,'NUM')=0 Then Do -- Say 'Argument 2 must be a number' Raise Syntax 88.902 array(2,e) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 3 must be a whole number between 1 and 999999' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 3 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(3,1,999999,xprec) End If b<0 & datatype(e,'W')=0 Then Return 'nan' return .my.rxm~power(b,e,xprec) ::routine rxmsqrt public Use Strict Arg x,xprec=(.my.rxm~precision) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End Select When x<0 Then Return 'nan' When x=0 Then Return 0 Otherwise return .my.rxm~sqrt(x,xprec) End ::routine rxmsin public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If wordpos(xtype,'R D G')=0 Then Do -- Say 'Argument 3 must be R, D, or G' Raise Syntax 88.907 array(3,'R, D, or G',xtype) End return .my.rxm~sin(x,xprec,xtype) ::routine rxmsinh public Use Strict Arg x,xprec=(.my.rxm~precision) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End return .my.rxm~sinh(x,xprec) ::routine rxmtan public Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End If wordpos(xtype,'R D G')=0 Then Do -- Say 'Argument 3 must be R, D, or G' Raise Syntax 88.907 array(3,'R, D, or G',xtype) End return .my.rxm~tan(x,xprec,xtype) ::routine rxmtanh public Use Strict Arg x,xprec=(.my.rxm~precision) If datatype(x,'NUM')=0 Then Do -- Say 'Argument 1 must be a number' Raise Syntax 88.902 array(1,x) End If datatype(xprec,'W')=0 Then Do -- Say 'Argument 2 must be a positive whole number' Raise Syntax 88.905 array(2,xprec) End If xprec<1 | 999999<xprec Then Do -- Say 'Argument 2 must be a whole number between 1 and 999999' Raise Syntax 88.907 array(2,1,999999,xprec) End return .my.rxm~tanh(x,xprec) ::routine rxmhelp public Use Arg xprec=(.my.rxm~precision),xtype=(.my.rxm~type) Say 'precision='xprec Say ' type='xtype Parse source s; Say ' source='s Parse version v; Say ' version='v Do si=2 To 5 Say substr(sourceline(si),3) End Say 'You can change the default precision and type as follows:' Say " .locaL~my.rxm~precision=50" Say " .locaL~my.rxm~type='R'" return 0  ## Oz declare PI = 3.14159265 fun {FromDegrees Deg} Deg * PI / 180. end fun {ToDegrees Rad} Rad * 180. / PI end Radians = PI / 4. Degrees = 45. in for F in [Sin Cos Tan] do {System.showInfo {F Radians}#" "#{F {FromDegrees Degrees}}} end for I#F in [Asin#Sin Acos#Cos Atan#Tan] do {System.showInfo {I {F Radians}}#" "#{ToDegrees {I {F Radians}}}} end  ## PARI/GP Pari accepts only radians; the conversion is simple but not included here. cos(Pi/2) sin(Pi/2) tan(Pi/2) acos(1) asin(1) atan(1)  {{works with|PARI/GP|2.4.3 and above}} apply(f->f(1), [cos,sin,tan,acos,asin,atan])  ## Pascal {{libheader|math}} Program TrigonometricFuntions(output); uses math; var radians, degree: double; begin radians := pi / 4.0; degree := 45; // Pascal works in radians. Necessary degree-radian conversions are shown. writeln (sin(radians),' ', sin(degree/180*pi)); writeln (cos(radians),' ', cos(degree/180*pi)); writeln (tan(radians),' ', tan(degree/180*pi)); writeln (); writeln (arcsin(sin(radians)),' Rad., or ', arcsin(sin(degree/180*pi))/pi*180,' Deg.'); writeln (arccos(cos(radians)),' Rad., or ', arccos(cos(degree/180*pi))/pi*180,' Deg.'); writeln (arctan(tan(radians)),' Rad., or ', arctan(tan(degree/180*pi))/pi*180,' Deg.'); // ( radians ) / pi * 180 = deg. end.  {{out}}  7.0710678118654750E-0001 7.0710678118654752E-0001 7.0710678118654755E-0001 7.0710678118654752E-0001 9.9999999999999994E-0001 1.0000000000000000E+0000 7.8539816339744828E-0001 Rad., or 4.5000000000000000E+0001 Deg. 7.8539816339744828E-0001 Rad., or 4.5000000000000000E+0001 Deg. 7.8539816339744828E-0001 Rad., or 4.5000000000000000E+0001 Deg.  ## Perl {{works with|Perl|5.8.8}} use Math::Trig; my angle_degrees = 45; my angle_radians = pi / 4; print sin(angle_radians), ' ', sin(deg2rad(angle_degrees)), "\n"; print cos(angle_radians), ' ', cos(deg2rad(angle_degrees)), "\n"; print tan(angle_radians), ' ', tan(deg2rad(angle_degrees)), "\n"; print cot(angle_radians), ' ', cot(deg2rad(angle_degrees)), "\n"; my asin = asin(sin(angle_radians)); print asin, ' ', rad2deg(asin), "\n"; my acos = acos(cos(angle_radians)); print acos, ' ', rad2deg(acos), "\n"; my atan = atan(tan(angle_radians)); print atan, ' ', rad2deg(atan), "\n"; my acot = acot(cot(angle_radians)); print acot, ' ', rad2deg(acot), "\n";  {{out}}  0.707106781186547 0.707106781186547 0.707106781186548 0.707106781186548 1 1 1 1 0.785398163397448 45 0.785398163397448 45 0.785398163397448 45 0.785398163397448 45  ## Perl 6 {{works with|Rakudo|2016.01}} say sin(pi/3); say cos(pi/4); say tan(pi/6); say asin(sqrt(3)/2); say acos(1/sqrt 2); say atan(1/sqrt 3);  ## Phix ?sin(PI/2) ?sin(90*PI/180) ?cos(0) ?cos(0*PI/180) ?tan(PI/4) ?tan(45*PI/180) ?arcsin(1)*2 ?arcsin(1)*180/PI ?arccos(0)*2 ?arccos(0)*180/PI ?arctan(1)*4 ?arctan(1)*180/PI  {{out}}  1 1 1 1 1.0 1.0 3.141592654 90 3.141592654 90 3.141592654 45  ## PHP radians = M_PI / 4; degrees = 45 * M_PI / 180; echo sin(radians) . " " . sin(degrees); echo cos(radians) . " " . cos(degrees); echo tan(radians) . " " . tan(degrees); echo asin(sin(radians)) . " " . asin(sin(radians)) * 180 / M_PI; echo acos(cos(radians)) . " " . acos(cos(radians)) * 180 / M_PI; echo atan(tan(radians)) . " " . atan(tan(radians)) * 180 / M_PI;  ## PicoLisp (load "@lib/math.l") (de dtor (Deg) (*/ Deg pi 180.0) ) (de rtod (Rad) (*/ Rad 180.0 pi) ) (prinl (format (sin (/ pi 4)) *Scl) " " (format (sin (dtor 45.0)) *Scl) ) (prinl (format (cos (/ pi 4)) *Scl) " " (format (cos (dtor 45.0)) *Scl) ) (prinl (format (tan (/ pi 4)) *Scl) " " (format (tan (dtor 45.0)) *Scl) ) (prinl (format (asin (sin (/ pi 4))) *Scl) " " (format (rtod (asin (sin (dtor 45.0)))) *Scl) ) (prinl (format (acos (cos (/ pi 4))) *Scl) " " (format (rtod (acos (cos (dtor 45.0)))) *Scl) ) (prinl (format (atan (tan (/ pi 4))) *Scl) " " (format (rtod (atan (tan (dtor 45.0)))) *Scl) )  {{out}} 0.707107 0.707107 0.707107 0.707107 1.000000 1.000000 0.785398 44.999986 0.785398 44.999986 0.785398 44.999986  ## PL/I  declare (x, xd, y, v) float; x = 0.5; xd = 45; /* angle in radians: */ v = sin(x); y = asin(v); put skip list (y); v = cos(x); y = acos(v); put skip list (y); v = tan(x); y = atan(v); put skip list (y); /* angle in degrees: */ v = sind(xd); put skip list (v); v = cosd(xd); put skip list (v); v = tand(xd); y = atand(v); put skip list (y); /* hyperbolic functions: */ v = sinh(x); put skip list (v); v = cosh(x); put skip list (v); v = tanh(x); y = atanh(v); put skip list (y);  Results:  5.00000E-0001 5.00000E-0001 5.00000E-0001 7.07107E-0001 7.07107E-0001 4.50000E+0001 5.21095E-0001 1.12763E+0000 5.00000E-0001  ## PL/SQL The transcendental functions COS, COSH, EXP, LN, LOG, SIN, SINH, SQRT, TAN, and TANH are accurate to 36 decimal digits. The transcendental functions ACOS, ASIN, ATAN, and ATAN2 are accurate to 30 decimal digits. DECLARE pi NUMBER := 4 * atan(1); radians NUMBER := pi / 4; degrees NUMBER := 45.0; BEGIN DBMS_OUTPUT.put_line(SIN(radians) || ' ' || SIN(degrees * pi/180) ); DBMS_OUTPUT.put_line(COS(radians) || ' ' || COS(degrees * pi/180) ); DBMS_OUTPUT.put_line(TAN(radians) || ' ' || TAN(degrees * pi/180) ); DBMS_OUTPUT.put_line(ASIN(SIN(radians)) || ' ' || ASIN(SIN(degrees * pi/180)) * 180/pi); DBMS_OUTPUT.put_line(ACOS(COS(radians)) || ' ' || ACOS(COS(degrees * pi/180)) * 180/pi); DBMS_OUTPUT.put_line(ATAN(TAN(radians)) || ' ' || ATAN(TAN(degrees * pi/180)) * 180/pi); end;  {{out}} ,7071067811865475244008443621048490392889 ,7071067811865475244008443621048490392893 ,7071067811865475244008443621048490392783 ,7071067811865475244008443621048490392779 1,00000000000000000000000000000000000001 1,00000000000000000000000000000000000002 ,7853981633974483096156608458198656891236 44,99999999999999999999999999999942521259 ,7853981633974483096156608458198857529988 45,00000000000000000000000000000057478811 ,7853981633974483096156608458198757210578 45,00000000000000000000000000000000000067  The following trigonometric functions are also available ATAN2(n1,n2) --Arctangent(y/x), -pi < result <= +pi SINH(n) --Hyperbolic sine COSH(n) --Hyperbolic cosine TANH(n) --Hyperbolic tangent  ## Pop11 Pop11 trigonometric functions accept both degrees and radians. In default mode argument is in degrees, after setting 'popradians' flag to 'true' arguments are in radians. sin(30) => cos(45) => tan(45) => arcsin(0.7) => arccos(0.7) => arctan(0.7) => ;;; switch to radians true -> popradians; sin(pi*30/180) => cos(pi*45/180) => tan(pi*45/180) => arcsin(0.7) => arccos(0.7) => arctan(0.7) =>  ## PostScript  90 sin = 60 cos = %tan of 45 degrees 45 sin 45 cos div = %inverse tan ( arc tan of sqrt 3) 3 sqrt 1 atan =  {{out}}  1.0 0.5 1.0 60.0  ## PowerShell {{Trans|C}} rad = [Math]::PI / 4 deg = 45 '{0,10} {1,10}' -f 'Radians','Degrees' '{0,10:N6} {1,10:N6}' -f [Math]::Sin(rad), [Math]::Sin(deg * [Math]::PI / 180) '{0,10:N6} {1,10:N6}' -f [Math]::Cos(rad), [Math]::Cos(deg * [Math]::PI / 180) '{0,10:N6} {1,10:N6}' -f [Math]::Tan(rad), [Math]::Tan(deg * [Math]::PI / 180) temp = [Math]::Asin([Math]::Sin(rad)) '{0,10:N6} {1,10:N6}' -f temp, (temp * 180 / [Math]::PI) temp = [Math]::Acos([Math]::Cos(rad)) '{0,10:N6} {1,10:N6}' -f temp, (temp * 180 / [Math]::PI) temp = [Math]::Atan([Math]::Tan(rad)) '{0,10:N6} {1,10:N6}' -f temp, (temp * 180 / [Math]::PI)  {{out}}  Radians Degrees 0,707107 0,707107 0,707107 0,707107 1,000000 1,000000 0,785398 45,000000 0,785398 45,000000 0,785398 45,000000  ===A More "PowerShelly" Way=== I would send the output as an array of objects containing the ([double]) properties: '''Radians''' and '''Degrees'''. Notice the difference between the last decimal place in the first two objects. If you were calculating coordinates as a civil engineer or land surveyor this difference could affect your measurments. Additionally, the output is an array of objects containing [double] values rather than an array of strings.  radians = [Math]::PI / 4 degrees = 45 [PSCustomObject]@{Radians=[Math]::Sin(radians); Degrees=[Math]::Sin(degrees * [Math]::PI / 180)} [PSCustomObject]@{Radians=[Math]::Cos(radians); Degrees=[Math]::Cos(degrees * [Math]::PI / 180)} [PSCustomObject]@{Radians=[Math]::Tan(radians); Degrees=[Math]::Tan(degrees * [Math]::PI / 180)} [double]tempVar = [Math]::Asin([Math]::Sin(radians)) [PSCustomObject]@{Radians=tempVar; Degrees=tempVar * 180 / [Math]::PI} [double]tempVar = [Math]::Acos([Math]::Cos(radians)) [PSCustomObject]@{Radians=tempVar; Degrees=tempVar * 180 / [Math]::PI} [double]tempVar = [Math]::Atan([Math]::Tan(radians)) [PSCustomObject]@{Radians=tempVar; Degrees=tempVar * 180 / [Math]::PI}  {{Out}}  Radians Degrees ------- ------- 0.707106781186547 0.707106781186547 0.707106781186548 0.707106781186548 1 1 0.785398163397448 45 0.785398163397448 45 0.785398163397448 45  ## PureBasic OpenConsole() Macro DegToRad(deg) deg*#PI/180 EndMacro Macro RadToDeg(rad) rad*180/#PI EndMacro degree = 45 radians.f = #PI/4 PrintN(StrF(Sin(DegToRad(degree)))+" "+StrF(Sin(radians))) PrintN(StrF(Cos(DegToRad(degree)))+" "+StrF(Cos(radians))) PrintN(StrF(Tan(DegToRad(degree)))+" "+StrF(Tan(radians))) arcsin.f = ASin(Sin(radians)) PrintN(StrF(arcsin)+" "+Str(RadToDeg(arcsin))) arccos.f = ACos(Cos(radians)) PrintN(StrF(arccos)+" "+Str(RadToDeg(arccos))) arctan.f = ATan(Tan(radians)) PrintN(StrF(arctan)+" "+Str(RadToDeg(arctan))) Input()  {{out}} 0.707107 0.707107 0.707107 0.707107 1.000000 1.000000 0.785398 45 0.785398 45 0.785398 45  ## Python Python's math module contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees. The math module also has degrees() and radians() functions for easy conversion. Python 3.2.2 (default, Sep 4 2011, 09:51:08) [MSC v.1500 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> from math import degrees, radians, sin, cos, tan, asin, acos, atan, pi >>> rad, deg = pi/4, 45.0 >>> print("Sine:", sin(rad), sin(radians(deg))) Sine: 0.7071067811865475 0.7071067811865475 >>> print("Cosine:", cos(rad), cos(radians(deg))) Cosine: 0.7071067811865476 0.7071067811865476 >>> print("Tangent:", tan(rad), tan(radians(deg))) Tangent: 0.9999999999999999 0.9999999999999999 >>> arcsine = asin(sin(rad)) >>> print("Arcsine:", arcsine, degrees(arcsine)) Arcsine: 0.7853981633974482 44.99999999999999 >>> arccosine = acos(cos(rad)) >>> print("Arccosine:", arccosine, degrees(arccosine)) Arccosine: 0.7853981633974483 45.0 >>> arctangent = atan(tan(rad)) >>> print("Arctangent:", arctangent, degrees(arctangent)) Arctangent: 0.7853981633974483 45.0 >>>  ## R deg <- function(radians) 180*radians/pi rad <- function(degrees) degrees*pi/180 sind <- function(ang) sin(rad(ang)) cosd <- function(ang) cos(rad(ang)) tand <- function(ang) tan(rad(ang)) asind <- function(v) deg(asin(v)) acosd <- function(v) deg(acos(v)) atand <- function(v) deg(atan(v)) r <- pi/3 rd <- deg(r) print( c( sin(r), sind(rd)) ) print( c( cos(r), cosd(rd)) ) print( c( tan(r), tand(rd)) ) S <- sin(pi/4) C <- cos(pi/3) T <- tan(pi/4) print( c( asin(S), asind(S) ) ) print( c( acos(C), acosd(C) ) ) print( c( atan(T), atand(T) ) )  ## Racket #lang racket (define radians (/ pi 4)) (define degrees 45) (displayln (format "~a ~a" (sin radians) (sin (* degrees (/ pi 180))))) (displayln (format "~a ~a" (cos radians) (cos (* degrees (/ pi 180))))) (displayln (format "~a ~a" (tan radians) (tan (* degrees (/ pi 180))))) (define arcsin (asin (sin radians))) (displayln (format "~a ~a" arcsin (* arcsin (/ 180 pi)))) (define arccos (acos (cos radians))) (displayln (format "~a ~a" arccos (* arccos (/ 180 pi)))) (define arctan (atan (tan radians))) (display (format "~a ~a" arctan (* arctan (/ 180 pi))))  ## RapidQ APPTYPE CONSOLE TYPECHECK ON SUB pause(prompt) PRINT prompt DO SLEEP .1 LOOP UNTIL LEN(INKEY) > 0 END SUB 'MAIN DEFDBL pi , radians , degrees , deg2rad pi = 4 * ATAN(1) deg2rad = pi / 180 radians = pi / 4 degrees = 45 * deg2rad PRINT format("%.6n" , SIN(radians)) + " " + format("%.6n" , SIN(degrees)) PRINT format("%.6n" , COS(radians)) + " " + format("%.6n" , COS(degrees)) PRINT format("%.6n" , TAN(radians)) + " " + format("%.6n" , TAN(degrees)) DEFDBL temp = SIN(radians) PRINT format("%.6n" , ASIN(temp)) + " " + format("%.6n" , ASIN(temp) / deg2rad) temp = COS(radians) PRINT format("%.6n" , ACOS(temp)) + " " + format("%.6n" , ACOS(temp) / deg2rad) temp = TAN(radians) PRINT format("%.6n" , ATAN(temp)) + " " + format("%.6n" , ATAN(temp) / deg2rad) pause("Press any key to continue.") END 'MAIN  ## REBOL REBOL [ Title: "Trigonometric Functions" URL: http://rosettacode.org/wiki/Trigonometric_Functions ] radians: pi / 4 degrees: 45.0 ; Unlike most languages, REBOL's trig functions work in degrees unless ; you specify differently. print [sine/radians radians sine degrees] print [cosine/radians radians cosine degrees] print [tangent/radians radians tangent degrees] d2r: func [ "Convert degrees to radians." d [number!] "Degrees" ][d * pi / 180] arcsin: arcsine sine degrees print [d2r arcsin arcsin] arccos: arccosine cosine degrees print [d2r arccos arccos] arctan: arctangent tangent degrees print [d2r arctan arctan]  {{out}} 0.707106781186547 0.707106781186547 0.707106781186548 0.707106781186548 1.0 1.0 0.785398163397448 45.0 0.785398163397448 45.0 0.785398163397448 45.0  ## REXX The REXX language doesn't have any trig functions (or for that matter, a square root [SQRT] function), so if higher math functions are wanted, you have to roll your own. Some of the normal/regular trigonometric functions are included here. ┌──────────────────────────────────────────────────────────────────────────┐ │ One common method that ensures enough accuracy in REXX is specifying │ │ more precision (via NUMERIC DIGITS nnn) than is needed, and then │ │ displaying the number of digits that are desired, or the number(s) │ │ could be re-normalized using the FORMAT BIF. │ │ │ │ The technique used (below) is to set the numeric digits ten higher │ │ than the desired digits, as specified by the SHOWDIGS variable. │ └──────────────────────────────────────────────────────────────────────────┘ Most math (POW, EXP, LOG, LN, GAMMA, etc.), trigonometric, and hyperbolic functions need only five extra digits, but ten extra digits is safer in case the argument is close to an asymptotic point or a multiple or fractional part of pi or somesuch. It should also be noted that both the '''pi''' and '''e''' constants have only around 77 decimal digits as included here, if more precision is needed, those constants should be extended. Both '''pi''' and '''e''' could've been shown with more precision, but having large precision numbers would add to this REXX program's length. If anybody wishes to see this REXX version of extended digits for '''pi''' or '''e''', I could extend them to any almost any precision (as a REXX constant). Normally, a REXX (external) subroutine is used for such purposes so as to not make the program using the constant unwieldy large. /*REXX program demonstrates some common trig functions (30 decimal digits are shown).*/ showdigs= 25 /*show only 25 digits of number. */ numeric digits showdigs + 10 /*DIGITS default is 9, but use */ /*extra digs to prevent rounding.*/ say 'Using' showdigs 'decimal digits precision.' /*show # decimal digs being used.*/ say do j=-180 to +180 by 15 /*let's just do a half─Monty. */ stuff = right(j, 4) 'degrees, rads=' show( d2r(j) ) , ' sin=' show( sinD(j) ) , ' cos=' show( cosD(J) ) /*don't let TANGENT go postal. */ if abs(j)\==90 then stuff=stuff ' tan=' show( tanD(j) ) say stuff end /*j*/ say do k=-1 to +1 by 1/2 /*keep the Arc─functions happy. */ say right(k, 4) 'radians, degs=' show( r2d(k) ) , ' Acos=' show( Acos(k) ) , ' Asin=' show( Asin(k) ) , ' Atan=' show( Atan(k) ) end /*k*/ exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a if a>1 then call AsinErr x /*X argument is out of range. */ if a >= sqrt(2) * .5 then return sign(x) * acos( sqrt(1 - aa), '-ASIN') do j=2 by 2 until p=z; p=z; o= o * aa * (j-1) / j; z= z +o / (j+1); end return z /* [↑] compute until no noise. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ Acos: procedure; parse arg x; if x<-1 | x>1 then call AcosErr; return pi()*.5 - Asin(x) AcosD: return r2d( Acos( arg(1) ) ) AsinD: return r2d( Asin( arg(1) ) ) cosD: return cos( d2r( arg(1) ) ) sinD: return sin( d2r( d2d( arg(1) ) ) ) tan: procedure; parse arg x; _= cos(x); if _=0 then call tanErr; return sin(x) / _ tanD: return tan( d2r( arg(1) ) ) d2d: return arg(1) // 360 /*normalize degrees ──► a unit circle*/ d2r: return r2r( d2d( arg(1) )*pi() / 180) /*convert degrees ──► radians. */ r2d: return d2d( ( arg(1) * 180 / pi() ) ) /*convert radians ──► degrees. */ r2r: return arg(1) // (pi() *2) /*normalize radians ──► a unit circle*/ show: return left( left('', arg(1) >= 0)format( arg(1), , showdigs) / 1, showdigs) tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13 tanErr: call tellErr 'tan(' || x") causes division by zero, X=" || x AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' || x AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' || x /*──────────────────────────────────────────────────────────────────────────────────────*/ Atan: procedure; parse arg x; if abs(x)=1 then return pi() * .25 * sign(x) return Asin(x / sqrt(1 + x*x) ) /*──────────────────────────────────────────────────────────────────────────────────────*/ cos: procedure; parse arg x; x= r2r(x); a= abs(x); hpi= pi * .5 numeric fuzz min(6, digits() - 3); if a=pi then return -1 if a=hpi | a=hpi*3 then return 0; if a=pi / 3 then return .5 if a=pi * 2 / 3 then return -.5; return .sinCos(1, -1) /*──────────────────────────────────────────────────────────────────────────────────────*/ sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, max(1, digits()-3)) if x=pi*.5 then return 1; if x==pi * 1.5 then return -1 if abs(x)=pi | x=0 then return 0; return .sinCos(x,1) /*──────────────────────────────────────────────────────────────────────────────────────*/ .sinCos: parse arg z 1 _,i; q= x*x do k=2 by 2 until p=z; p= z; _= - _ * q / (k * (k+i) ); z= z + _; end return z /*──────────────────────────────────────────────────────────────────────────────────────*/ sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9; h= d+6 numeric digits; numeric form; if x<0 then do; x= -x; i= 'i'; end parse value format(x, 2, 1, , 0) 'E0' with g 'E' _ .; g= g *.5'e'_ % 2 do j=0 while h>9; m.j=h; h= h % 2 + 1; end /*j*/ do k=j+5 to 0 by -1; numeric digits m.k; g= (g+x/g) * .5; end /*k*/ numeric digits d; return (g/1)i /*make complex if X < 0.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ e: e = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535 return e /*Note: the actual E subroutine returns E's accuracy that */ /*matches the current NUMERIC DIGITS, up to 1 million digits.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix= ix + sign(x); x=x - ix z=1; _=1; w=z; do j=1; _= _*x/j; z= (z+_) / 1; if z==w then leave; w=z; end if z\==0 then z= e()**ix * z; return z /*──────────────────────────────────────────────────────────────────────────────────────*/ pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078164062862 return pi /*Note: the actual PI subroutine returns PI's accuracy that */ /*matches the current NUMERIC DIGITS, up to 1 million digits.*/ /*John Machin's formula is used for calculating more digits. */  Programming note: ╔═════════════════════════════════════════════════════════════════════════════╗ ║ Functions that are not included here are (among others): ║ ║ ║ ║ some of the usual higher-math functions normally associated with trig ║ ║ functions: POW, GAMMA, LGGAMMA, ERF, ERFC, ROOT, ATAN2, ║ ║ LOG (LN), LOG2, LOG10, and all of the ║ ║ hyperbolic trigonometric functions and their inverses (too many to list ║ ║ here), ║ ║ angle conversions/normalizations: degrees/radians/grads/mils: ║ ║ a circle ≡ 2 pi radians ≡ 360 degrees ≡ 400 grads ≡ 6400 mils. ║ ║ ║ ║ Some of the other trigonometric functions are (hyphens added intentionally):║ ║ ║ ║ CHORD ║ ║ COT (co-tangent) ║ ║ CSC (co-secant) ║ ║ CVC (co-versed cosine) ║ ║ CVS (co-versed sine) ║ ║ CXS (co-exsecant) ║ ║ HAC (haver-cosine) ║ ║ HAV (haver-sine ║ ║ SEC (secant) ║ ║ VCS (versed cosine or ver-cosine) ║ ║ VSN (versed sine or ver-sine) ║ ║ XCS (ex-secant) ║ ║ COS/SIN/TAN cardinal (damped COS/SIN/TAN functions) ║ ║ COS/SIN integral ║ ║ ║ ║ and all pertinent inverses of the above functions (AVSN, ACVS, ···). ║ ╚═════════════════════════════════════════════════════════════════════════════╝ {{out|output}} (Shown at three-quarter size.) BigDecimal class. BigMath only has big versions of sine, cosine, and arctangent; so we must implement tangent, arcsine and arccosine. {{trans|bc}} {{works with|Ruby|1.9}} ruby require 'bigdecimal' # BigDecimal require 'bigdecimal/math' # BigMath include BigMath # Allow sin(x, prec) instead of BigMath.sin(x, prec). # Tangent of _x_. def tan(x, prec) sin(x, prec) / cos(x, prec) end # Arcsine of _y_, domain [-1, 1], range [-pi/2, pi/2]. def asin(y, prec) # Handle angles with no tangent. return -PI / 2 if y == -1 return PI / 2 if y == 1 # Tangent of angle is y / x, where x^2 + y^2 = 1. atan(y / sqrt(1 - y * y, prec), prec) end # Arccosine of _x_, domain [-1, 1], range [0, pi]. def acos(x, prec) # Handle angle with no tangent. return PI / 2 if x == 0 # Tangent of angle is y / x, where x^2 + y^2 = 1. a = atan(sqrt(1 - x * x, prec) / x, prec) if a < 0 a + PI(prec) else a end end prec = 52 pi = PI(prec) degrees = pi / 180 # one degree in radians b1 = BigDecimal.new "1" b2 = BigDecimal.new "2" b3 = BigDecimal.new "3" f = proc { |big| big.round(50).to_s('F') } print("Using radians:", "\n sin(-pi / 6) = ", f[ sin(-pi / 6, prec) ], "\n cos(3 * pi / 4) = ", f[ cos(3 * pi / 4, prec) ], "\n tan(pi / 3) = ", f[ tan(pi / 3, prec) ], "\n asin(-1 / 2) = ", f[ asin(-b1 / 2, prec) ], "\n acos(-sqrt(2) / 2) = ", f[ acos(-sqrt(b2, prec) / 2, prec) ], "\n atan(sqrt(3)) = ", f[ atan(sqrt(b3, prec), prec) ], "\n") print("Using degrees:", "\n sin(-30) = ", f[ sin(-30 * degrees, prec) ], "\n cos(135) = ", f[ cos(135 * degrees, prec) ], "\n tan(60) = ", f[ tan(60 * degrees, prec) ], "\n asin(-1 / 2) = ", f[ asin(-b1 / 2, prec) / degrees ], "\n acos(-sqrt(2) / 2) = ", f[ acos(-sqrt(b2, prec) / 2, prec) / degrees ], "\n atan(sqrt(3)) = ", f[ atan(sqrt(b3, prec), prec) / degrees ], "\n")  {{out}} txt Using radians: sin(-pi / 6) = -0.5 cos(3 * pi / 4) = -0.70710678118654752440084436210484903928483593768847 tan(pi / 3) = 1.73205080756887729352744634150587236694280525381038 asin(-1 / 2) = -0.52359877559829887307710723054658381403286156656252 acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953133 atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312504 Using degrees: sin(-30) = -0.5 cos(135) = -0.70710678118654752440084436210484903928483593768847 tan(60) = 1.73205080756887729352744634150587236694280525381038 asin(-1 / 2) = -30.0 acos(-sqrt(2) / 2) = 135.0 atan(sqrt(3)) = 60.0  ## Run BASIC runbasic ' Find these three ratios: Sine, Cosine, Tangent. (These ratios have NO units.) deg = 45.0 ' Run BASIC works in radians; so, first convert deg to rad as shown in next line. rad = deg * (atn(1)/45) print "Ratios for a "; deg; " degree angle, (or "; rad; " radian angle.)" print "Sine: "; SIN(rad) print "Cosine: "; COS(rad) print "Tangent: "; TAN(rad) print "Inverse Functions - - (Using above ratios)" ' Now, use those ratios to work backwards to show their original angle in radians. ' Also, use this: rad / (atn(1)/45) = deg (To change radians to degrees.) print "Arcsine: "; ASN(SIN(rad)); " radians, (or "; ASN(SIN(rad))/(atn(1)/45); " degrees)" print "Arccosine: "; ACS(COS(rad)); " radians, (or "; ACS(COS(rad))/(atn(1)/45); " degrees)" print "Arctangent: "; ATN(TAN(rad)); " radians, (or "; ATN(TAN(rad))/(atn(1)/45); " degrees)" ' This code also works in Liberty BASIC. ' The above (atn(1)/45) = approx .01745329252  {{out}} txt Ratios for a 45.0 degree angle, (or 0.785398163 radian angle.) Sine: 0.707106781 Cosine: 0.707106781 Tangent: 1.0 Inverse Functions - - (Using above ratios) Arcsine: 0.785398163 radians, (or 45.0 degrees) Arccosine: 0.785398163 radians, (or 45.0 degrees) Arctangent: 0.785398163 radians, (or 45.0 degrees)  ## SAS sas data _null_; pi = 4*atan(1); deg = 30; rad = pi/6; k = pi/180; x = 0.2; a = sin(rad); b = sin(deg*k); put a b; a = cos(rad); b = cos(deg*k); put a b; a = tan(rad); b = tan(deg*k); put a b; a=arsin(x); b=arsin(x)/k; put a b; a=arcos(x); b=arcos(x)/k; put a b; a=atan(x); b=atan(x)/k; put a b; run;  ## Scala {{libheader|Scala}} Scala import scala.math._ object Gonio extends App { //Pi / 4 rad is 45 degrees. All answers should be the same. val radians = Pi / 4 val degrees = 45.0 println(s"{sin(radians)} {sin(toRadians(degrees))}") //cosine println(s"{cos(radians)} {cos(toRadians(degrees))}") //tangent println(s"{tan(radians)} {tan(toRadians(degrees))}") //arcsine val bgsin = asin(sin(radians)) println(s"bgsin {toDegrees(bgsin)}") val bgcos = acos(cos(radians)) println(s"bgcos {toDegrees(bgcos)}") //arctangent val bgtan = atan(tan(radians)) println(s"bgtan {toDegrees(bgtan)}") val bgtan2 = atan2(1, 1) println(s"bgtan {toDegrees(bgtan)}") }  ## Scheme scheme (define pi (* 4 (atan 1))) (define radians (/ pi 4)) (define degrees 45) (display (sin radians)) (display " ") (display (sin (* degrees (/ pi 180)))) (newline) (display (cos radians)) (display " ") (display (cos (* degrees (/ pi 180)))) (newline) (display (tan radians)) (display " ") (display (tan (* degrees (/ pi 180)))) (newline) (define arcsin (asin (sin radians))) (display arcsin) (display " ") (display (* arcsin (/ 180 pi))) (newline) (define arccos (acos (cos radians))) (display arccos) (display " ") (display (* arccos (/ 180 pi))) (newline) (define arctan (atan (tan radians))) (display arctan) (display " ") (display (* arctan (/ 180 pi))) (newline)  ## Seed7 The example below uses the libaray [http://seed7.sourceforge.net/libraries/math.htm math.s7i], which defines, besides many other functions, [http://seed7.sourceforge.net/libraries/math.htm#sin%28ref_float%29 sin], [http://seed7.sourceforge.net/libraries/math.htm#cos%28ref_float%29 cos], [http://seed7.sourceforge.net/libraries/math.htm#tan%28ref_float%29 tan], [http://seed7.sourceforge.net/libraries/math.htm#asin%28ref_float%29 asin], [http://seed7.sourceforge.net/libraries/math.htm#acos%28ref_float%29 acos] and [http://seed7.sourceforge.net/libraries/math.htm#atan%28ref_float%29 atan]. seed7  include "seed7_05.s7i"; include "float.s7i"; include "math.s7i"; const proc: main is func local const float: radians is PI / 4.0; const float: degrees is 45.0; begin writeln(" radians degrees"); writeln("sine: " <& sin(radians) digits 5 <& sin(degrees * PI / 180.0) digits 5 lpad 9); writeln("cosine: " <& cos(radians) digits 5 <& cos(degrees * PI / 180.0) digits 5 lpad 9); writeln("tangent: " <& tan(radians) digits 5 <& tan(degrees * PI / 180.0) digits 5 lpad 9); writeln("arcsine: " <& asin(0.70710677) digits 5 <& asin(0.70710677) * 180.0 / PI digits 5 lpad 9); writeln("arccosine: " <& acos(0.70710677) digits 5 <& acos(0.70710677) * 180.0 / PI digits 5 lpad 9); writeln("arctangent: " <& atan(1.0) digits 5 <& atan(1.0) * 180.0 / PI digits 5 lpad 9); end func;  {{out}} txt radians degrees sine: 0.70711 0.70711 cosine: 0.70711 0.70711 tangent: 1.00000 1.00000 arcsine: 0.78540 45.00000 arccosine: 0.78540 45.00000 arctangent: 0.78540 45.00000  ## Sidef ruby var angle_deg = 45; var angle_rad = Num.pi/4; for arr in [ [sin(angle_rad), sin(deg2rad(angle_deg))], [cos(angle_rad), cos(deg2rad(angle_deg))], [tan(angle_rad), tan(deg2rad(angle_deg))], [cot(angle_rad), cot(deg2rad(angle_deg))], ] { say arr.join(" "); } for n in [ asin(sin(angle_rad)), acos(cos(angle_rad)), atan(tan(angle_rad)), acot(cot(angle_rad)), ] { say [n, rad2deg(n)].join(' '); }  {{out}} txt 0.707106781186547 0.707106781186547 0.707106781186548 0.707106781186548 1 1 1 1 0.785398163397448 45 0.785398163397448 45 0.785398163397448 45 0.785398163397448 45  ## SQL PL {{works with|Db2 LUW}} With SQL only: sql pl --Conversion values degrees(3.1415926); values radians(180); -- This is equal to Pi. --PI/4 45 values sin(radians(180)/4); values sin(radians(45)); values cos(radians(180)/4); values cos(radians(45)); values tan(radians(180)/4); values tan(radians(45)); values cot(radians(180)/4); values cot(radians(45)); values asin(sin(radians(180)/4)); values asin(sin(radians(45))); values atan(tan(radians(180)/4)); values atan(tan(radians(45))); --PI/3 60 values sin(radians(180)/3); values sin(radians(60)); values cos(radians(180)/3); values cos(radians(60)); values tan(radians(180)/3); values tan(radians(60)); values cot(radians(180)/3); values cot(radians(60)); values asin(sin(radians(180)/3)); values asin(sin(radians(60))); values atan(tan(radians(180)/3)); values atan(tan(radians(60)));  Output: txt db2 -tx values degrees(3.1415926) +1.79999996929531E+002 values radians(180) +3.14159265358979E+000 values sin(radians(180)/4) +7.07106781186547E-001 values sin(radians(45)) +7.07106781186547E-001 values cos(radians(180)/4) +7.07106781186548E-001 values cos(radians(45)) +7.07106781186548E-001 values tan(radians(180)/4) +1.00000000000000E+000 values tan(radians(45)) +1.00000000000000E+000 values cot(radians(180)/4) +1.00000000000000E+000 values cot(radians(45)) +1.00000000000000E+000 values asin(sin(radians(180)/4)) +7.85398163397448E-001 values asin(sin(radians(45))) +7.85398163397448E-001 values atan(tan(radians(180)/4)) +7.85398163397448E-001 values atan(tan(radians(45))) +7.85398163397448E-001 values sin(radians(180)/3) +8.66025403784439E-001 values sin(radians(60)) +8.66025403784439E-001 values cos(radians(180)/3) +5.00000000000000E-001 values cos(radians(60)) +5.00000000000000E-001 values tan(radians(180)/3) +1.73205080756888E+000 values tan(radians(60)) +1.73205080756888E+000 values cot(radians(180)/3) +5.77350269189626E-001 values cot(radians(60)) +5.77350269189626E-001 values asin(sin(radians(180)/3)) +1.04719755119660E+000 values asin(sin(radians(60))) +1.04719755119660E+000 values atan(tan(radians(180)/3)) +1.04719755119660E+000 values atan(tan(radians(60))) +1.04719755119660E+000  ## Stata Stata computes only in radians, but the conversion is easy. stata scalar deg=_pi/180 display cos(30*deg) display sin(30*deg) display tan(30*deg) display cos(_pi/6) display sin(_pi/6) display tan(_pi/6) display acos(0.5) display asin(0.5) display atan(0.5)  ## Tcl The built-in functions only take radian arguments. tcl package require Tcl 8.5 proc PI {} {expr {4*atan(1)}} proc deg2rad d {expr {d/180*[PI]}} proc rad2deg r {expr {r*180/[PI]}} namespace path ::tcl::mathfunc proc trig degrees { set radians [deg2rad degrees] puts [sin radians] puts [cos radians] puts [tan radians] set arcsin [asin [sin radians]]; puts "arcsin [rad2deg arcsin]" set arccos [acos [cos radians]]; puts "arccos [rad2deg arccos]" set arctan [atan [tan radians]]; puts "arctan [rad2deg arctan]" } trig 60.0  txt 0.8660254037844386 0.5000000000000001 1.7320508075688767 1.0471975511965976 59.99999999999999 1.0471975511965976 59.99999999999999 1.0471975511965976 59.99999999999999  ## VBA vb Public Sub trig() Pi = WorksheetFunction.Pi() Debug.Print Sin(Pi / 2) Debug.Print Sin(90 * Pi / 180) Debug.Print Cos(0) Debug.Print Cos(0 * Pi / 180) Debug.Print Tan(Pi / 4) Debug.Print Tan(45 * Pi / 180) Debug.Print WorksheetFunction.Asin(1) * 2 Debug.Print WorksheetFunction.Asin(1) * 180 / Pi Debug.Print WorksheetFunction.Acos(0) * 2 Debug.Print WorksheetFunction.Acos(0) * 180 / Pi Debug.Print Atn(1) * 4 Debug.Print Atn(1) * 180 / Pi End Sub  {{out}} txt 1 1 1 1 1 1 3,14159265358979 90 3,14159265358979 90 3,14159265358979 45  ## Visual Basic .NET {{trans|C#}} vbnet Module Module1 Sub Main() Console.WriteLine(" ### radians ") Console.WriteLine(" sin (pi/3) = {0}", Math.Sin(Math.PI / 3)) Console.WriteLine(" cos (pi/3) = {0}", Math.Cos(Math.PI / 3)) Console.WriteLine(" tan (pi/3) = {0}", Math.Tan(Math.PI / 3)) Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5)) Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5)) Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5)) Console.WriteLine() Console.WriteLine(" ### degrees ") Console.WriteLine(" sin (60) = {0}", Math.Sin(60 * Math.PI / 180)) Console.WriteLine(" cos (60) = {0}", Math.Cos(60 * Math.PI / 180)) Console.WriteLine(" tan (60) = {0}", Math.Tan(60 * Math.PI / 180)) Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5) * 180 / Math.PI) Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5) * 180 / Math.PI) Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5) * 180 / Math.PI) End Sub End Module  {{out}} txt ### radians sin (pi/3) = 0.866025403784439 cos (pi/3) = 0.5 tan (pi/3) = 1.73205080756888 arcsin (1/2) = 0.523598775598299 arccos (1/2) = 1.0471975511966 arctan (1/2) = 0.463647609000806 ### degrees sin (60) = 0.866025403784439 cos (60) = 0.5 tan (60) = 1.73205080756888 arcsin (1/2) = 30 arccos (1/2) = 60 arctan (1/2) = 26.565051177078  ## XPL0 XPL0 include c:\cxpl\codes; \intrinsic 'code' declarations def Pi = 3.14159265358979323846; func real ATan(Y); \Arc tangent real Y; return ATan2(Y, 1.0); func real Deg(X); \Convert radians to degrees real X; return 57.2957795130823 * X; func real Rad(X); \Convert degrees to radians real X; return X / 57.2957795130823; real A, B, C; [A:= Sin(Pi/6.0); RlOut(0, A); ChOut(0, 9\tab$$;  RlOut(0, Sin(Rad(30.0)));  CrLf(0);
B:= Cos(Pi/6.0);
RlOut(0, B);  ChOut(0, 9\tab\);  RlOut(0, Cos(Rad(30.0)));  CrLf(0);
C:= Tan(Pi/4.0);
RlOut(0, C);  ChOut(0, 9\tab\);  RlOut(0, Tan(Rad(45.0)));  CrLf(0);

RlOut(0, ASin(A));  ChOut(0, 9\tab\);  RlOut(0, Deg(ASin(A)));  CrLf(0);
RlOut(0, ACos(B));  ChOut(0, 9\tab\);  RlOut(0, Deg(ACos(B)));  CrLf(0);
RlOut(0, ATan(C));  ChOut(0, 9\tab\);  RlOut(0, Deg(ATan(C)));  CrLf(0);
]


{{out}}

txt

0.50000         0.50000
0.86603         0.86603
1.00000         1.00000
0.52360        30.00000
0.52360        30.00000
0.78540        45.00000



## zkl

zkl

(0.523599).sin()      //-->0.5
etc

(0.5).asin()         //-->0.523599
(0.5).acos()         //-->1.0472
(1.0).atan()         //-->0.785398
(1.0).atan().toDeg() //-->45
etc