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.
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;
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.
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.
$radians = deg2rad($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 (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.