#
# Trigonometric functions, mostly inherited from Math::Complex.
# -- Jarkko Hietaniemi, April 1997
# -- Raphael Manfredi, September 1996 (indirectly: because of Math::Complex)
#
require Exporter;
package Math::Trig;
use strict;
use Math::Complex qw(:trig);
use vars qw($VERSION $PACKAGE
@ISA
@EXPORT);
@ISA = qw(Exporter);
$VERSION = 1.00;
my @angcnv = qw(rad2deg rad2grad
deg2rad deg2grad
grad2rad grad2deg);
@EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}},
@angcnv);
use constant pi2 => 2 * pi;
use constant DR => pi2/360;
use constant RD => 360/pi2;
use constant DG => 400/360;
use constant GD => 360/400;
use constant RG => 400/pi2;
use constant GR => pi2/400;
#
# Truncating remainder.
#
sub remt ($$) {
# Oh yes, POSIX::fmod() would be faster. Possibly. If it is available.
$_[0] - $_[1] * int($_[0] / $_[1]);
}
#
# Angle conversions.
#
sub rad2deg ($) { remt(RD * $_[0], 360) }
sub deg2rad ($) { remt(DR * $_[0], pi2) }
sub grad2deg ($) { remt(GD * $_[0], 360) }
sub deg2grad ($) { remt(DG * $_[0], 400) }
sub rad2grad ($) { remt(RG * $_[0], 400) }
sub grad2rad ($) { remt(GR * $_[0], pi2) }
=head1 NAME
Math::Trig - trigonometric functions
=head1 SYNOPSIS
use Math::Trig;
$x = tan(0.9);
$y = acos(3.7);
$z = asin(2.4);
$halfpi = pi/2;
$rad = deg2rad(120);
=head1 DESCRIPTION
C defines many trigonometric functions not defined by the
core Perl which defines only the C and C. The constant
B is also defined as are a few convenience functions for angle
conversions.
=head1 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 B is also defined.
$pi2 = 2 * pi;
=head2 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 C, C, C, C, C, C, C,
C, C, the argument cannot be C<0> (zero). For the
C, C, the argument cannot be C<1> (one). For the
C, C, the argument cannot be C<-1> (minus one). For the
C, C, C, C, the argument cannot be I, where I is any integer.
=head2 SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS
Please note that some of the trigonometric functions can break out
from the B into the B. For example
C 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 L) as input for the
trigonometric functions might produce as output results that no more
are simple real numbers: instead they are complex numbers.
The C handles this by using the C package
which knows how to handle complex numbers, please see L
for more information. In practice you need not to worry about getting
complex numbers as results because the C 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 C<1.571>
and the imaginary part of approximately C<-1.317>.
=head1 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 I radians or I<360> degrees or I<400> gradians.
=head1 BUGS
Saying C