Math::Trig - trigonometric functions

- NAME
- SYNOPSIS
- DESCRIPTION
- TRIGONOMETRIC FUNCTIONS
  - ERRORS DUE TO DIVISION BY ZERO
  - SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS
- ANGLE CONVERSIONS
- BUGS
- AUTHORS

# 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 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 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 `` (zero). For the `atanh`, `acoth`, the argument cannot be `1` (one). For the `atanh`, `acoth`, the argument cannot be `-1` (minus 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>.