Math::Trig(3)							 Math::Trig(3)

NAME    [Toc]    [Back]

     Math::Trig	- trigonometric	functions

SYNOPSIS    [Toc]    [Back]

	     use Math::Trig;

	     $x	= tan(0.9);
	     $y	= acos(3.7);
	     $z	= asin(2.4);

	     $halfpi = pi/2;

	     $rad = deg2rad(120);

DESCRIPTION    [Toc]    [Back]

     Math::Trig	defines	many trigonometric functions not defined by the	core
     Perl which	defines	only the sin() and cos().  The constant	pi is also
     defined as	are a few convenience functions	for angle conversions.

TRIGONOMETRIC FUNCTIONS    [Toc]    [Back]

     The tangent

	     tan

     The cofunctions of	the sine, cosine, and tangent (cosec/csc and cotan/cot
     are aliases)

	     csc cosec sec cot cotan

     The arcus (also known as the inverse) functions of	the sine, cosine, and
     tangent

	     asin acos atan

     The principal value of the	arc tangent of y/x

	     atan2(y, x)

     The arcus cofunctions of the sine,	cosine,	and tangent (acosec/acsc and
     acotan/acot are aliases)

	     acsc acosec asec acot acotan

     The hyperbolic sine, cosine, and tangent

	     sinh cosh tanh

     The cofunctions of	the hyperbolic sine, cosine, and tangent (cosech/csch
     and cotanh/coth are aliases)





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Math::Trig(3)							 Math::Trig(3)



	     csch cosech sech coth cotanh

     The arcus (also known as the inverse) functions of	the hyperbolic sine,
     cosine, and tangent

	     asinh acosh atanh

     The arcus cofunctions of the hyperbolic sine, cosine, and tangent
     (acsch/acosech and	acoth/acotanh are aliases)

	     acsch acosech asech acoth acotanh

     The trigonometric constant	pi is also defined.

	     $pi2 = 2 *	pi;


     ERRORS DUE	TO DIVISION BY ZERO

     The following functions

	     tan
	     sec
	     csc
	     cot
	     asec
	     acsc
	     tanh
	     sech
	     csch
	     coth
	     atanh
	     asech
	     acsch
	     acoth

     cannot be computed	for all	arguments because that would mean dividing by
     zero or taking logarithm of zero. These situations	cause fatal runtime
     errors looking like this

	     cot(0): Division by zero.
	     (Because in the definition	of cot(0), the divisor sin(0) is 0)
	     Died at ...

     or

	     atanh(-1):	Logarithm of zero.
	     Died at...

     For the csc, cot, asec, acsc, acot, csch, coth, asech, acsch, the
     argument cannot be	0 (zero).  For the atanh, acoth, the argument cannot
     be	1 (one).  For the atanh, acoth,	the argument cannot be -1 (minus one).



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Math::Trig(3)							 Math::Trig(3)



     For the tan, sec, tanh, sech, the argument	cannot be pi/2 + k * pi, where
     k is any integer.

     SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS

     Please note that some of the trigonometric	functions can break out	from
     the real axis into	the complex plane. For example asin(2) has no
     definition	for plain real numbers but it has definition for complex
     numbers.

     In	Perl terms this	means that supplying the usual Perl numbers (also
     known as scalars, please see the perldata manpage)	as input for the
     trigonometric functions might produce as output results that no more are
     simple real numbers: instead they are complex numbers.

     The Math::Trig handles this by using the Math::Complex package which
     knows how to handle complex numbers, please see the Math::Complex manpage
     for more information. In practice you need	not to worry about getting
     complex numbers as	results	because	the Math::Complex takes	care of
     details like for example how to display complex numbers. For example:

	     print asin(2), "\n";

     should produce something like this	(take or leave few last	decimals):

	     1.5707963267949-1.31695789692482i

     That is, a	complex	number with the	real part of approximately 1.571 and
     the imaginary part	of approximately -1.317.

ANGLE CONVERSIONS    [Toc]    [Back]

     (Plane, 2-dimensional) angles may be converted with the following
     functions.

	     $radians  = deg2rad($degrees);
	     $radians  = grad2rad($gradians);

	     $degrees  = rad2deg($radians);
	     $degrees  = grad2deg($gradians);

	     $gradians = deg2grad($degrees);
	     $gradians = rad2grad($radians);

     The full circle is	2 pi radians or	360 degrees or 400 gradians.

BUGS    [Toc]    [Back]

     Saying use	Math::Trig; exports many mathematical routines in the caller
     environment and even overrides some (sin, cos).  This is construed	as a
     feature by	the Authors, actually... ;-)






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Math::Trig(3)							 Math::Trig(3)



     The code is not optimized for speed, especially because we	use
     Math::Complex and thus go quite near complex numbers while	doing the
     computations even when the	arguments are not. This, however, cannot be
     completely	avoided	if we want things like asin(2) to give an answer
     instead of	giving a fatal runtime error.

AUTHORS    [Toc]    [Back]

     Jarkko Hietaniemi <jhi@iki.fi> and	Raphael	Manfredi
     <Raphael_Manfredi@grenoble.hp.com>.


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