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);

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

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)

        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. 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 ...

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

(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 the caller environment and even overrides some (sin, cos). This is construed as a feature by the Authors, actually... ;-)

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

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

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