sin, cos, ... - Maple Programming Help

sin, cos, ...

The Trigonometric functions

sinh, cosh, ...

The Hyperbolic functions

 Calling Sequence sin(x)    cos(x)    tan(x) sec(x)    csc(x)    cot(x) sinh(x)   cosh(x)   tanh(x) sech(x)   csch(x)   coth(x)

Parameters

 x - expression

Description

 • Arguments for all trigonometric functions

 cosecant cosine cotangent secant sine tangent

 and hyperbolic functions

 csch cosh coth sech sinh tanh

 • 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].

Examples

Evaluating trigonometric expressions.

 > $\mathrm{sin}\left(0\right)$
 ${0}$ (1)
 > $\mathrm{cos}\left(\frac{\mathrm{\pi }}{3}\right)$
 $\frac{{1}}{{2}}$ (2)
 > $\mathrm{sec}\left(\frac{\mathrm{\pi }}{3}\right)$
 ${2}$ (3)
 > $\mathrm{coth}\left(3.1+2.5I\right)$
 ${1.001144421}{+}{0.003896610899}{}{I}$ (4)
 > $\mathrm{sin}\left(\frac{7}{60}\mathrm{\pi }\right)$
 ${\mathrm{sin}}{}\left(\frac{{7}{}{\mathrm{\pi }}}{{60}}\right)$ (5)
 > $r≔\mathrm{convert}\left(,'\mathrm{radical}'\right)$
 ${r}{≔}\left(\frac{\sqrt{{3}}}{{8}}{+}\frac{{1}}{{8}}\right){}\sqrt{{5}{-}\sqrt{{5}}}{-}\frac{\sqrt{{2}}{}\left(\sqrt{{5}}{+}{1}\right){}\sqrt{{3}}}{{16}}{+}\frac{\sqrt{{2}}{}\left(\sqrt{{5}}{+}{1}\right)}{{16}}$ (6)
 > $\mathrm{evalf}\left(\right)$
 ${0.3583679496}$ (7)

Expanding and simplifying trigonometric functions.

 > $\mathrm{simplify}\left({\mathrm{sin}\left(x\right)}^{2}+{\mathrm{cos}\left(x\right)}^{2},\mathrm{trig}\right)$
 ${1}$ (8)
 > $\mathrm{expand}\left(\mathrm{sin}\left(x+y\right)\right)$
 ${\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({y}\right){+}{\mathrm{cos}}{}\left({x}\right){}{\mathrm{sin}}{}\left({y}\right)$ (9)
 > $\mathrm{combine}\left(,\mathrm{trig}\right)$
 ${\mathrm{sin}}{}\left({x}{+}{y}\right)$ (10)
 > $\mathrm{expand}\left(\mathrm{sin}\left(2x\right)\right)$
 ${2}{}{\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right)$ (11)

Other operations involving trigonometric functions.

 > $\mathrm{convert}\left(\mathrm{tanh}\left(x\right),\mathrm{exp}\right)$
 $\frac{{{ⅇ}}^{{x}}{-}{{ⅇ}}^{{-}{x}}}{{{ⅇ}}^{{x}}{+}{{ⅇ}}^{{-}{x}}}$ (12)
 > $\mathrm{D}\left(\mathrm{tan}\right)$
 ${{\mathrm{tan}}}^{{2}}{+}{1}$ (13)
 > $\mathrm{int}\left(\mathrm{sec}\left(x\right),x\right)$
 ${\mathrm{ln}}{}\left({\mathrm{sec}}{}\left({x}\right){+}{\mathrm{tan}}{}\left({x}\right)\right)$ (14)
 > $\mathrm{solve}\left(\mathrm{csc}\left(x\right)=1,x\right)$
 $\frac{{\mathrm{\pi }}}{{2}}$ (15)
 > $\mathrm{discont}\left(\mathrm{tan}\left(x+\frac{\mathrm{\pi }}{2}\right),x\right)$
 $\left\{{\mathrm{\pi }}{}{\mathrm{_Z1~}}\right\}$ (16)