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Math::Trig

Section: Perl Programmers Reference Guide (3)
Updated: perl 5.004, patch 04
Index 

NAME

Math::Trig - trigonometric functions 

SYNOPSIS

        use Math::Trig;                $x = tan(0.9);        $y = acos(3.7);        $z = asin(2.4);                $halfpi = pi/2;

        $rad = deg2rad(120);

 

DESCRIPTION

Math::Trig defines many trigonometric functions not defined by thecore Perl which defines only the sin() and cos(). The constantpi is also defined as are a few convenience functions for angleconversions. 

TRIGONOMETRIC FUNCTIONS

The tangent

        tan

The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cotare 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/acscand 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/cschand cotanh/coth are aliases)

        csch cosech sech coth cotanh

The arcus (also known as the inverse) functions of the hyperbolicsine, 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 dividingby zero or taking logarithm of zero. These situations cause fatalruntime 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 theatanh, acoth, the argument cannot be 1 (one). For theatanh, acoth, the argument cannot be -1 (minus one). For thetan, 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 outfrom the real axis into the complex plane. For exampleasin(2) has no definition for plain real numbers but it hasdefinition for complex numbers.

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

The Math::Trig handles this by using the Math::Complex packagewhich knows how to handle complex numbers, please see the Math::Complex manpagefor more information. In practice you need not to worry about gettingcomplex numbers as results because the Math::Complex takes care ofdetails 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 1.571and the imaginary part of approximately -1.317. 

ANGLE CONVERSIONS

(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

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

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

AUTHORS

Jarkko Hietaniemi <jhiAATTiki.fi> and Raphael Manfredi <Raphael_ManfrediAATTgrenoble.hp.com>.

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Index

NAME

SYNOPSIS

DESCRIPTION

TRIGONOMETRIC FUNCTIONS

ERRORS DUE TO DIVISION BY ZERO

SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS

ANGLE CONVERSIONS

BUGS

AUTHORS

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