## 4.9 Complex hyperbolic trigonometric functions

The standard hyperbolic trigonometric functions are supported for complex numbers.

complex cosh(complex z)
Return the complex hyperbolic cosine of z, $\begin{equation*} \textrm{cosh}(z) = \frac{\exp(z) + \exp(-z)} {2}. \end{equation*}$
Available since 2.28

complex sinh(complex z)
Return the complex hyperbolic sine of z, $\begin{equation*} \textrm{sinh}(z) = \frac{\displaystyle \exp(z) - \exp(-z)} {\displaystyle 2}. \end{equation*}$
Available since 2.28

complex tanh(complex z)
Return the complex hyperbolic tangent of z, $\begin{equation*} \textrm{tanh}(z) \ = \ \frac{\textrm{sinh}(z)} {\textrm{cosh}(z)} \ = \ \frac{\displaystyle \exp(z) - \exp(-z)} {\displaystyle \exp(z) + \exp(-z)}. \end{equation*}$
Available since 2.28

complex acosh(complex z)
Return the complex hyperbolic arc (inverse) cosine of z, $\begin{equation*} \textrm{acosh}(z) = \log(z + \sqrt{(z + 1)(z - 1)}). \end{equation*}$
Available since 2.28

complex asinh(complex z)
Return the complex hyperbolic arc (inverse) sine of z, $\begin{equation*} \textrm{asinh}(z) = \log(z + \sqrt{1 + z^2}). \end{equation*}$
Available since 2.28

complex atanh(complex z)
Return the complex hyperbolic arc (inverse) tangent of z, $\begin{equation*} \textrm{atanh}(z) = \frac{\log(1 + z) - \log(1 - z)} {2}. \end{equation*}$
Available since 2.28