Math::Trig(3) Math::Trig(3)
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)
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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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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
(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... ;-)
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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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