Arguments for all trigonometric functions

and hyperbolic functions

must be given in radians.  (1 radian = 180/Pi degrees).

For trigonometric functions that accept arguments in degrees, see trigd.

Maple also provides simplification and expansion procedures that apply most of the common trigonometric and hyperbolic identities. Also available are conversion routines that will convert trigonometric expressions to other forms. Three examples are that (1) any trigonometric expression can be converted to an expression in terms of only sin and cos, (2) expressions involving exp(x) can be converted to their hyperbolic forms, and (3) a trigonometric function with an argument of the form $q\mathrm{\pi }$, where q is a rational, can in some cases be converted to radical form. For more help, see convert.

For information about expanding and simplifying trigonometric expressions, see expand, factor, combine/trig, and simplify/trig.

$\sin \left(0\right)$

$0$

$\cos \left(\frac{\mathrm{\pi }}{3}\right)$

$\frac{1}{2}$

$\sec \left(\frac{\mathrm{\pi }}{3}\right)$

$2$

$\coth \left(3.1+2.5\mathrm{I}\right)$

$1.001144421+0.003896610899\mathrm{I}$

$\sin \left(\frac{7}{60}\mathrm{\pi }\right)$

$\sin \left(\frac{7\mathrm{\pi }}{60}\right)$

$r≔\mathrm{convert}\left(\,'\mathrm{radical}'\right)$

$r≔\left(\frac{\sqrt{3}}{8}+\frac{1}{8}\right)\sqrt{5-\sqrt{5}}-\frac{\sqrt{2}\left(\sqrt{5}+1\right)\sqrt{3}}{16}+\frac{\sqrt{2}\left(\sqrt{5}+1\right)}{16}$

$\mathrm{evalf}\left(r\right)$

$0.3583679496$

$\mathrm{simplify}\left({\sin \left(x\right)}^2+{\cos \left(x\right)}^2\,\mathrm{trig}\right)$

$1$

$\mathrm{expand}\left(\sin \left(x+y\right)\right)$

$\sin \left(x\right)\cos \left(y\right)+\cos \left(x\right)\sin \left(y\right)$

$\mathrm{combine}\left(\,\mathrm{trig}\right)$

$\sin \left(x+y\right)$

$\mathrm{expand}\left(\sin \left(2x\right)\right)$

$2\sin \left(x\right)\cos \left(x\right)$

$\mathrm{convert}\left(\tanh \left(x\right)\,\exp \right)$

$\frac{{\ⅇ}^x-{\ⅇ}^{-x}}{{\ⅇ}^x+{\ⅇ}^{-x}}$

$\mathrm{D}\left(\tan \right)$

${\tan }^2+1$

$\mathrm{int}\left(\sec \left(x\right)\,x\right)$

$\ln \left(\sec \left(x\right)+\tan \left(x\right)\right)$

$\mathrm{solve}\left(\csc \left(x\right)=1\,x\right)$

$\frac{\mathrm{\pi }}{2}$

$\mathrm{discont}\left(\tan \left(x+\frac{\mathrm{\pi }}{2}\right)\,x\right)$

$\left\{\mathrm{\pi }\mathrm{\_Z1~}\right\}$