Math::Trig(3)
NNAAMMEE
Math::Trig - trigonometric functions
SSYYNNOOPPSSIISS
use Math::Trig;
$x = tan(0.9);
$y = acos(3.7);
$z = asin(2.4);
$halfpi = pi/2;
$rad = deg2rad(120);
DDEESSCCRRIIPPTTIIOONN
Math::Trig defines many trigonometric functions not
defined by the core Perl which defines only the sin() and
cos(). The constant ppii is also defined as are a few
convenience functions for angle conversions.
TTRRIIGGOONNOOMMEETTRRIICC FFUUNNCCTTIIOONNSS
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 ppii is also defined.
$pi2 = 2 * pi;
EERRRROORRSS DDUUEE TTOO DDIIVVIISSIIOONN BBYY ZZEERROO
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.
SSIIMMPPLLEE ((RREEAALL)) AARRGGUUMMEENNTTSS,, CCOOMMPPLLEEXX RREESSUULLTTSS
Please note that some of the trigonometric functions can
break out from the rreeaall aaxxiiss into the ccoommpplleexx ppllaannee. 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.
AANNGGLLEE CCOONNVVEERRSSIIOONNSS
(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.
BBUUGGSS
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.
AAUUTTHHOORRSS
Jarkko Hietaniemi lt;jhi@iki.fi and Raphael Manfredi
lt;Raphael_Manfredi@grenoble.hp.com.