Trigonometry Library

<?php
    // PHP Mathematics Library - Trigonometry
    //
    // Copyright (c) 2008, reusablecode.blogspot.com; some rights reserved.
    //
    // This work is licensed under the Creative Commons Attribution License. To view
    // a copy of this license, visit http://creativecommons.org/licenses/by/3.0/ or
    // send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California
    // 94305, USA.
 
    // CIRCULAR FUNCTIONS
 
    // There are six basic trigonometric functions, three of which (sine, cosine, and tangent) are already defined in PHP.
    // function sin() - Returns the sine of the specified angle.
    // function cos() - Returns the cosine of the specified angle.
    // function tan() - Returns the tangent of the specified angle.
 
    // The other three basic trigonometric functions are the multiplicative inverses of the previous three functions.
 
    // Returns the cosecant of the specified angle.
    function csc($x)
    {
        return (1 / sin($x));
    }
 
    // Returns the secant of the specified angle.
    function sec($x)
    {
        return (1 / cos($x));
    }
 
    // Returns the cotangent of the specified angle.
    function cot($x)
    {
        return (1 / tan($x));
    }
 
    // The following trigonometric functions are rarely used anymore, but are included in this function library for completeness.
 
    // Returns the versed sine (also called versine) of the specified angle.
    function versin($x)
    {
        return (1 - cos($x));
    }
 
    // Returns the coversed sine (also called coversine) of the specified angle.
    function coversin($x)
    {
        return (1 - sin($x));
    }
 
    // Returns the haversed sine (also called haversine) of the specified angle.
    function haversin($x)
    {
        return (versin($x) / 2);
    }
 
    // Returns the hacoversed sine (also called hacoversine, cohaversine, or havercosine) of the specified angle.
    function hacoversin($x)
    {
        return (coversin($x) / 2);
    }
 
    // Returns the exsecant of the specified angle.
    function exsec($x)
    {
        return (sec($x) - 1);
    }
 
    // Returns the excosecant of the specified angle.
    function excsc($x)
    {
        return (csc($x) - 1);
    }
 
    // Each of the six basic trigonometric functions also has an inverse function, three of which are already defined in PHP.
    // function asin() - Returns the angle whose sine is the specified whole number.
    // function acos() - Returns the angle whose cosine is the specified number.
    // function atan() - Returns the angle whose tangent is the specified number.
 
    // Returns the angle whose cosecant is the specified number.
    function acsc($x)
    {
        return (atan($x / sqrt($x * $x - 1)) + (sin($x) - 1) * (2 * atan(1)));
    }
 
    // Returns the angle whose secant is the specified number.
    function asec($x)
    {
        return (atan($x / sqr($x * $x - 1)) + sin(($x) - 1) * (2 * atan(1)));
    }
 
    // Returns the angle whose cotangent is the specified number.
    function acot($x)
    {
        return (atan($x) + 2 * atan(1));
    }
 
    // HYPERBOLIC FUNCTIONS
 
    // The hyperbolic functions are like the basic trigonometric functions, but for hyperbola instead of circles.
    // function sinh() - Returns the hyperbolic sine of the specified angle.
    // function cosh() - Returns the hyperbolic cosine of the specified angle.
    // function tanh() - Returns the hyperbolic tangent of the specified angle.
 
    // Returns the hyperbolic cosecant of the specified angle.
    function csch($x)
    {
        return (2 / (exp($x) - exp(-$x)));
    }
 
    // Returns the hyperbolic secant of the specified angle.
    function sech($x)
    {
        return (2 / (exp($x) + exp(-$x)));
    }
 
    // Returns the hyperbolic cotangent of the specified angle.
    function coth($x)
    {
        return (exp($x) + exp(-$x)) / (exp($x) - exp(-$x));
    }
 
    // Just like in trigonometry, the six basic hyperbolic functions have inverse functions.
    // function asinh() - Returns the angle whose hyperbolic sine is the specified number.
    // function acosh() - Returns the angle whose hyperbolic cosine is the specified number.
    // function atanh() - Returns the angle whose hyperbolic tangent is the specified number.
 
    // Returns the angle whose hyperbolic cosecant is the specified number.
    function acsch($x)
    {
        return (log((sin($x) * sqrt($x * $x + 1) + 1) / $x));
    }
 
    // Returns the angle whose hyperbolic secant is the specified number.
    function asech($x)
    {
        return (log((sqrt(-$x * $x + 1) + 1) / $x));
    }
 
    // Returns the angle whose hyperbolic cotangent is the specified number.
    function acoth($x)
    {
        return (log(($x + 1) / ($x - 1)) / 2);
    }
 
 
    // GUDERMANNIAN FUNCTIONS
 
    // The Gudermannian function relates the circular and hyperbolic trigonometric functions without resorting to complex numbers.
    function gd($x)
    {
        return (2 * atan(tanh($x / 2)));
    }
 
    // Like other trigonometric and hyperbolic functions, Gudermannian has an inverse.
    function agd($x)
    {
        return atanh(sin($x));
    }
?>