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Tim Bunce

# NAME

Math::Trig - trigonometric functions

# SYNOPSIS

``````        use Math::Trig;

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

\$halfpi = pi/2;

# 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 `0` (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 perldata) 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 Math::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);

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.