- TRIGONOMETRIC FUNCTIONS
- ANGLE CONVERSIONS
Math::Trig - trigonometric functions
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
cos(). The constant pi is also defined as are a few convenience functions for angle conversions.
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
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 ...
atanh(-1): Logarithm of zero. Died at...
acsch, the argument cannot be
0 (zero). For the
acoth, the argument cannot be
1 (one). For the
acoth, the argument cannot be
-1 (minus one). For the
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.
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):
That is, a complex number with the real part of approximately
1.571 and the imaginary part of approximately
(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.
use Math::Trig; exports many mathematical routines in the caller environment and even overrides some (
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.
Jarkko Hietaniemi <email@example.com> and Raphael Manfredi <Raphael_Manfredi@grenoble.hp.com>.