2 # Trigonometric functions, mostly inherited from Math::Complex.
3 # -- Jarkko Hietaniemi, April 1997
4 # -- Raphael Manfredi, September 1996 (indirectly: because of Math::Complex)
12 use Math::Complex qw(:trig);
14 use vars qw($VERSION $PACKAGE
22 my @angcnv = qw(rad_to_deg rad_to_grad
23 deg_to_rad deg_to_grad
24 grad_to_rad grad_to_deg);
26 @EXPORT = (@{$Math::Complex::EXPORT_TAGS{'trig'}},
29 use constant pi2 => 2 * pi;
30 use constant DR => pi2/360;
31 use constant RD => 360/pi2;
32 use constant DG => 400/360;
33 use constant GD => 360/400;
34 use constant RG => 400/pi2;
35 use constant GR => pi2/400;
38 # Truncating remainder.
42 # Oh yes, POSIX::fmod() would be faster. Possibly. If it is available.
43 $_[0] - $_[1] * int($_[0] / $_[1]);
50 sub rad_to_deg ($) { remt(RD * $_[0], 360) }
52 sub deg_to_rad ($) { remt(DR * $_[0], pi2) }
54 sub grad_to_deg ($) { remt(GD * $_[0], 360) }
56 sub deg_to_grad ($) { remt(DG * $_[0], 400) }
58 sub rad_to_grad ($) { remt(RG * $_[0], 400) }
60 sub grad_to_rad ($) { remt(GR * $_[0], pi2) }
64 Math::Trig - trigonometric functions
76 $rad = deg_to_rad(120);
80 C<Math::Trig> defines many trigonometric functions not defined by the
81 core Perl which defines only the C<sin()> and C<cos()>. The constant
82 B<pi> is also defined as are a few convenience functions for angle
85 =head1 TRIGONOMETRIC FUNCTIONS
91 The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot
94 csc cosec sec cot cotan
96 The arcus (also known as the inverse) functions of the sine, cosine,
101 The principal value of the arc tangent of y/x
105 The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc
106 and acotan/acot are aliases)
108 acsc acosec asec acot acotan
110 The hyperbolic sine, cosine, and tangent
114 The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch
115 and cotanh/coth are aliases)
117 csch cosech sech coth cotanh
119 The arcus (also known as the inverse) functions of the hyperbolic
120 sine, cosine, and tangent
124 The arcus cofunctions of the hyperbolic sine, cosine, and tangent
125 (acsch/acosech and acoth/acotanh are aliases)
127 acsch acosech asech acoth acotanh
129 The trigonometric constant B<pi> is also defined.
133 =head2 ERRORS DUE TO DIVISION BY ZERO
135 The following functions
152 cannot be computed for all arguments because that would mean dividing
153 by zero. These situations cause fatal runtime errors looking like this
155 cot(0): Division by zero.
156 (Because in the definition of cot(0), the divisor sin(0) is 0)
159 For the C<csc>, C<cot>, C<asec>, C<acsc>, C<csch>, C<coth>, C<asech>,
160 C<acsch>, the argument cannot be C<0> (zero). For the C<atanh>,
161 C<acoth>, the argument cannot be C<1> (one). For the C<tan>, C<sec>,
162 C<tanh>, C<sech>, the argument cannot be I<pi/2 + k * pi>, where I<k> is
165 =head2 SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS
167 Please note that some of the trigonometric functions can break out
168 from the B<real axis> into the B<complex plane>. For example
169 C<asin(2)> has no definition for plain real numbers but it has
170 definition for complex numbers.
172 In Perl terms this means that supplying the usual Perl numbers (also
173 known as scalars, please see L<perldata>) as input for the
174 trigonometric functions might produce as output results that no more
175 are simple real numbers: instead they are complex numbers.
177 The C<Math::Trig> handles this by using the C<Math::Complex> package
178 which knows how to handle complex numbers, please see L<Math::Complex>
179 for more information. In practice you need not to worry about getting
180 complex numbers as results because the C<Math::Complex> takes care of
181 details like for example how to display complex numbers. For example:
185 should produce something like this (take or leave few last decimals):
187 1.5707963267949-1.31695789692482i
189 That is, a complex number with the real part of approximately C<1.571>
190 and the imaginary part of approximately C<-1.317>.
192 =head1 ANGLE CONVERSIONS
194 (Plane, 2-dimensional) angles may be converted with the following functions.
196 $radians = deg_to_rad($degrees);
197 $radians = grad_to_rad($gradians);
199 $degrees = rad_to_deg($radians);
200 $degrees = grad_to_deg($gradians);
202 $gradians = deg_to_grad($degrees);
203 $gradians = rad_to_grad($radians);
205 The full circle is 2 I<pi> radians or I<360> degrees or I<400> gradians.
209 Saying C<use Math::Trig;> exports many mathematical routines in the
210 caller environment and even overrides some (C<sin>, C<cos>). This is
211 construed as a feature by the Authors, actually... ;-)
213 The code is not optimized for speed, especially because we use
214 C<Math::Complex> and thus go quite near complex numbers while doing
215 the computations even when the arguments are not. This, however,
216 cannot be completely avoided if we want things like C<asin(2)> to give
217 an answer instead of giving a fatal runtime error.
221 Jarkko Hietaniemi <F<jhi@iki.fi>>
222 Raphael Manfredi <F<Raphael_Manfredi@grenoble.hp.com>>