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 *    Trigonometric Functions and their Derivatives

In mathematics trigonometric functions are functions of an angle. They relate the length of the sides of a triangle to the angles. The most common trigonometric functions are sine, cosine and tangent, though cosecant, secant, and cotangent are also commonly used. The standard unit circle has a radius of 1 and in that context the sine of an angle gives the y-value(rise) of the created triangle and cos gives the x-value(run) of the created triangle. The most important trigonometric functions are sin and cos, all others can be derived from those two. tan( q  ) = sin(  q  )/cos(  q  ) csc( q  ) = 1/sin(  q  ) sec( q  ) = 1/cos(  q  ) cot( q  ) = 1/tan(  q  ) A cofunction of a given trig function (f) is, the function obtained after the complement its parameter is taken. Since the complement of any angle q  is 90° - q , then sine(90° - q ) = cosine( q ) secant(90° - q ) = cosecant( q ) tangent(90° - q ) = cotangent( q )  = q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">arccosecant(hyp/opp) = q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> || = q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">arcsecant(hyp/adj) = q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> || = q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">arccotangent(adj/opp) = q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> sine ( q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">) = opp/hyp || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">cosecant( q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">) = hyp/opp  ||
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;"> cosine ( q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">) = adj/hyp || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">secant( q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">) = hyp/adj  ||
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">tangent( q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">) = opp/adj || <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">cotangent( q <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">) = adj/opp  ||
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">inverse functions  ||
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">arcsine(opp/hyp)
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">arccosine(adj/hyp)
 * <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 12pt;">arctangent(opp/adj)