use Math::Trig; $x = tan(0.9); $y = acos(3.7); $z = asin(2.4); $halfpi = pi/2;
$rad = deg2rad(120);
The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot are aliases)
csc, cosec, sec, 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.
acoth acsc acsch asec asech atanh cot coth csc csch sec sech tan tanhcannot 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.
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):
1.5707963267949-1.31695789692482iThat 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.
You can import radial coordinate conversion functions by using the :radial tag:
use Math::Trig ':radial';
($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z); ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z); ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z); ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z); ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi); ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);All angles are in radians.
Spherical coordinates, (rho, theta, pi), are three-dimensional coordinates which define a point in three-dimensional space. They are based on a sphere surface. The radius of the sphere is rho, also known as the radial coordinate. The angle in the xy-plane (around the z-axis) is theta, also known as the azimuthal coordinate. The angle from the z-axis is phi, also known as the polar coordinate. The `North Pole' is therefore 0, 0, rho, and the `Bay of Guinea' (think of the missing big chunk of Africa) 0, pi/2, rho.
Beware: some texts define theta and phi the other way round, some texts define the phi to start from the horizontal plane, some texts use r in place of rho.
Cylindrical coordinates, (rho, theta, z), are three-dimensional coordinates which define a point in three-dimensional space. They are based on a cylinder surface. The radius of the cylinder is rho, also known as the radial coordinate. The angle in the xy-plane (around the z-axis) is theta, also known as the azimuthal coordinate. The third coordinate is the z, pointing up from the theta-plane.
($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z);
($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z);
($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z);
($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z);Notice that when $z is not 0 $rho_s is not equal to $rho_c.
($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi);
($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi);Notice that when $z is not 0 $rho_c is not equal to $rho_s.
use Math::Trig 'great_circle_distance'
$distance = great_circle_distance($theta0, $phi0, $theta1, $phi, [, $rho]);The great circle distance is the shortest distance between two points on a sphere. The distance is in $rho units. The $rho is optional, it defaults to 1 (the unit sphere), therefore the distance defaults to radians.
use Math::Trig qw(great_circle_distance deg2rad);
# Notice the 90 - latitude: phi zero is at the North Pole. @L = (deg2rad(-0.5), deg2rad(90 - 51.3)); @T = (deg2rad(139.8),deg2rad(90 - 35.7));
$km = great_circle_distance(@L, @T, 6378);The answer may be off by up to 0.3% because of the irregular (slightly aspherical) form of the Earth.
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.