\section{acosh---Hyperbolic Arc Cosine}
\label{fn:acosh}
\index{acosh()}
\index{hyperbolic arc cosine}
\index{inverse hyperbolic cosine}
\index{hyperbolic cosine!inverse}
\begin{rail}
ACosh : 'acosh' '(' ( Scalar | Matrix ) ')' ;
\end{rail}

\verb+acosh+ returns the hyperbolic arc cosine of the argument. The return
value is expressed in radians.  If the argument is a matrix, the operation
is performed element-by-element.

$\Longrightarrow$ This is not an \RLaB\ built-in function.  This function
is normally loaded on start-up from the \verb+acosh.r+ file in the
standard \verb+rlib+ directory. Use of the \verb+-r+ option, incorrectly 
setting the \verb+RLAB_LIB_DIR+ environmental variable, or modifying
\verb+acosh.r+ may make this function unavailable.


\paragraph{Example}
\index{example of acosh()}
\index{acosh()!example}
\begin{verbatim}
> acosh(0)
        0 + 1.57i
> acosh(1+1j)
     1.06 + 0.905i
> acosh(1)
        0
> Mat = (rand(2,3)+rand(2,3)*(0+1j))*5 
 Mat =
 matrix columns 1 thru 3
               5 + 3.32i            3.24 + 1.02i           0.185 + 3.27i
           4.87 + 0.423i           1.67 + 0.837i          0.809 + 0.644i

> acosh(Mat)
 matrix columns 1 thru 3
           2.48 + 0.593i            1.9 + 0.319i             1.9 + 1.52i
          2.27 + 0.0885i           1.28 + 0.531i          0.751 + 0.897i
\end{verbatim}

See also: Page~\pageref{fn:acos} \verb+acos()+,
Page~\pageref{fn:asinh} \verb+asinh()+,
Page~\pageref{fn:atanh} \verb+atanh()+,
Page~\pageref{fn:cosh} \verb+cosh()+,
Page~\pageref{fn:sinh} \verb+sinh()+,
Page~\pageref{fn:tanh} \verb+tanh()+.

\newpage 



