Just another update
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Ingy döt Net
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@ -1 +1,7 @@
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If your language has a library or built-in functions for trigonometry, show examples of sine, cosine, tangent, and their inverses 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]].
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If your language has a library or built-in functions for trigonometry, show examples of sine, cosine, tangent, and their inverses using the same angle in radians and degrees.
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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).
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For the inverse functions, use the same number and convert its answer to radians and degrees.
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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]].
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@ -1,2 +1,4 @@
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---
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category:
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- Mathematics
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note: Arithmetic operations
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@ -0,0 +1,3 @@
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sin(Pi/3);
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cos(Pi/3);
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tan(Pi/3);
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@ -0,0 +1,4 @@
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with(Units[Standard]):
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sin(60*Unit(degree));
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cos(60*Unit(degree));
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tan(60*Unit(degree));
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@ -0,0 +1,3 @@
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csc(Pi/3);
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sec(Pi/3);
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cot(Pi/3);
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@ -0,0 +1,3 @@
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arcsin(1);
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arccos(1);
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arctan(1);
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@ -9,7 +9,7 @@ say 'Using' showdigs 'decimal digits precision.'; say
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' sin='show(sinD(j)),
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' cos='show(cosD(J))
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/*don't let TAN go postal.*/
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if abs(j)\==90 then stuff=stuff ' tan='show(tanD(j))
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if abs(j)\==90 then stuff=stuff ' tan='show(tanD(j))
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say stuff
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end /*j*/
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@ -21,48 +21,51 @@ say; do k=-1 to +1 by 1/2 /*keep the Arc-functions happy. */
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end /*k*/
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────subroutines─────────────────────────*/
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Asin: procedure; parse arg x 1 z 1 o 1 p; if x<-1 | x>1 then call AsinErr
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s=x*x; if abs(x)>=sqrt(2)*.5 then return sign(x)*Acos(sqrt(1-s))
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do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=p then leave; p=z; end
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return z
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Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a
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if a>1 then call $81r -1,1,x,"ASIN" /*X arg is out of range.*/
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if a>=sqrt(2)*.5 then return sign(x)*acos(sqrt(1-aa), '-ASIN')
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do j=2 by 2 until p=z; p=z; o=o*aa*(j-1)/j; z=z+o/(j+1); end
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return z /* [↑] compute until no noise.*/
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Atan: procedure; parse arg x; if abs(x)=1 then return pi()*.25*sign(x)
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return Asin(x/sqrt(1+x*x))
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Atan: procedure; parse arg x; if abs(x)=1 then return pi() * .25 * sign(x)
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return Asin(x/sqrt(1+x*x) )
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cos: procedure; parse arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9)
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if a=pi() then return -1; if a=pi()*.5 | a=pi()*2 then return 0
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pi3=pi()/3; if a=pi3 then return .5; if a=2*pi3 then return -.5
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if a=pi then return -1; if a=pi*.5 | a=pi*2 then return 0
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pi3=pi/3; if a=pi3 then return .5; if a=2*pi3 then return -.5
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return .sinCos(1,1,-1)
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sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5,digits()-3)
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if abs(x)=pi() then return 0; return .sinCos(x,x,1)
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sin: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)
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if x=pi*.5 then return 1; if x==pi*1.5 then return -1
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if abs(x)=pi | x=0 then return 0; return .sinCos(x, x, +1)
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.sinCos: parse arg z 1 p,_,i; x=x*x
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do k=2 by 2; _=-_*x/(k*(k+i));z=z+_;if z=p then leave;p=z;end; return z
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.sinCos: parse arg z,_,i; x=x*x
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do k=2 by 2 until p=z; p=z; _=-_*x/(k*(k+i)); z=z+_; end /*k*/
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return z
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sqrt: procedure; parse arg x; if x=0 then return 0; m.=9; p=digits(); i=
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numeric digits 9; if x<0 then do; x=-x; i='i'; end; numeric form; m.0=p
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'E'_%2; m.1=p
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do j=2 while p>9; m.j=p; p=p%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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numeric digits m.0; return (g/1)i
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e: return,
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2.7182818284590452353602874713526624977572470936999595749669676277240766303535
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/*Note: the actual E subroutine returns E's accuracy that */
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sqrt: procedure; parse arg x,i; if x=0 then return 0; d=digits(); m.=11
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if x<0 then i='i'; numeric digits 11; numeric form; p=d+d%4+2
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'E'_%2
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do j=0 while p>9; m.j=p; p=p%2+1; end /*j*/
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do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k
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g=.5*(g+x/g); end /*k*/; numeric digits d; return g/1
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e: e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535
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return e /*Note: the actual E subroutine returns E's accuracy that */
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/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
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/*If more than 1 million digits are required, be patient. */
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exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x=x-ix
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z=1; _=1; w=z; do j=1; _=_*x/j; z=(z+_)/1; if z==w then leave; w=z; end
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if z\==0 then z=e()**ix*z; return z
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z=1; _=1; w=z; do j=1; _=_*x/j; z=(z+_)/1; if z==w then leave; w=z; end
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if z\==0 then z=e()**ix*z; return z
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pi: return, /*a bit of overkill, but hey !! */
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3.1415926535897932384626433832795028841971693993751058209749445923078164062862
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/*Note: the actual PI subroutine returns PI's accuracy that */
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pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862
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return pi /*Note: the actual PI subroutine returns PI's accuracy that */
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/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
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/*John Machin's formula is used for calculating more digits. */
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/*If more than 1 million digits are required, be patient. */
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$fuzz: return min(arg(1), max(1, digits() - arg(2) ) )
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Acos: procedure; parse arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x)
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AcosD: return r2d(Acos(arg(1)))
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AsinD: return r2d(Asin(arg(1)))
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@ -70,40 +73,13 @@ cosD: return cos(d2r(arg(1)))
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sinD: return sin(d2r(d2d(arg(1))))
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tan: procedure; parse arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
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tanD: return tan(d2r(arg(1)))
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d2d: return arg(1)//360 /*normalize degrees►1 unit circle. */
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d2r: return r2r(d2d(arg(1))*pi()/180) /*convert degrees ──► radians. */
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r2d: return d2d((arg(1)*180/pi())) /*convert radians ──► degrees. */
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r2r: return arg(1)//(pi()*2) /*normalize radians ──►a unit circle*/
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d2d: return arg(1) // 360 /*normalize degrees►1 unit circle. */
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d2r: return r2r(d2d(arg(1))*pi() /180) /*convert degrees ──► radians. */
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r2d: return d2d((arg(1)*180 /pi())) /*convert radians ──► degrees. */
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r2r: return arg(1) // (pi()*2) /*normalize radians ──►a unit circle*/
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show: return left(left('',arg(1)>=0)format(arg(1),,showdigs)/1,showdigs)
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tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13
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tanErr: call tellErr 'tan('||x") causes division by zero, X="||x
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AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X='||x
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AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X='||x
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sqrtErr: call tellErr "sqrt(x), X can't be negative, X="||x
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/* ┌───────────────────────────────────────────────────────────────┐
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│ Not included here are (among others): │
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│ some of the usual higher-math functions normally associated │
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│ with trig functions: POW, GAMMA, LGGAMMA, ERF, ERFC, ROOT, │
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│ LOG (LN), LOG2, LOG10, ATAN2, │
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│ all of the hyperbolic trig functions and their inverses, │
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│ (too many to name here). │
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│ Angle conversions/normalizations: degrees/radians/grads/mils │
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│ [a circle = 2 pi radians, 360 degrees, 400 grads, 6400 mils].│
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│ Some of the other trig functions are (hyphens were added │
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│ intentionally): │
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│ CHORD │
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│ COT (co-tangent) │
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│ CSC (co-secant) │
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│ CVC (co-versed cosine) │
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│ CVS (co-versed sine) │
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│ CXS (co-exsecant) │
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│ HAC (haver-cosine) │
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│ HAV (haver-sine │
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│ SEC (secant) │
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│ VCS (versed cosine or vercosine) │
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│ VSN (versed sine or versine) │
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│ XCS (exsecant) │
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│ COS/SIN/TAN cardinal (damped COS/SIN/TAN function) │
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│ COS/SIN integral │
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│ and all pertinent of the above's inverses (AVSN, ACVS...) │
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└───────────────────────────────────────────────────────────────┘ */
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tanErr: call tellErr 'tan('||x") causes division by zero, X=" || x
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AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' || x
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AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' || x
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sqrtErr: call tellErr "sqrt(x), X can't be negative, X=" || x
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@ -0,0 +1,23 @@
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import scala.math._
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object Gonio extends App {
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//Pi / 4 rad is 45 degrees. All answers should be the same.
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val radians = Pi / 4
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val degrees = 45.0
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println(s"${sin(radians)} ${sin(toRadians(degrees))}")
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//cosine
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println(s"${cos(radians)} ${cos(toRadians(degrees))}")
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//tangent
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println(s"${tan(radians)} ${tan(toRadians(degrees))}")
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//arcsine
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val bgsin = asin(sin(radians))
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println(s"$bgsin ${toDegrees(bgsin)}")
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val bgcos = acos(cos(radians))
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println(s"$bgcos ${toDegrees(bgcos)}")
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//arctangent
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val bgtan = atan(tan(radians))
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println(s"$bgtan ${toDegrees(bgtan)}")
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val bgtan2 = atan2(1, 1)
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println(s"$bgtan ${toDegrees(bgtan)}")
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}
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