\section{asin --- Arc Sine}
\label{fn:asin}
\index{asin()}
\index{arc sine}
\index{sine!inverse}
\begin{rail}
ArcSine : 'asin' '(' ( Scalar | Matrix ) ')' ;
\end{rail}

\verb+asin+ returns the arc sine of the argument. The return value is 
expressed in radians, in the range $[ -\pi/2, \pi/2 ]$.  It is an error
if the argument is real and the magnitude of the argument is greater
than $1$.  If the argument is a matrix, the operation is performed
element by element. 


\paragraph{Example}
\index{example of asin()}
\index{asin()!example}
\begin{verbatim}
> asin(1)
     1.57
> asin(0)
        0
> asin(-1)
    -1.57
> asin(0.5)
    0.524
> asin(0+0.5j)
        0 + 0.481i
> asin(0.5+0.5j)
    0.452 + 0.531i
> Mat = (rand(2,3)+rand(2,3)*(0+1j))
 Mat =
 matrix columns 1 thru 3
              1 + 0.665i          0.647 + 0.204i         0.0369 + 0.655i
         0.975 + 0.0847i          0.333 + 0.167i          0.162 + 0.129i

> asin(Mat)
 matrix columns 1 thru 3
          0.806 + 0.853i          0.677 + 0.259i         0.0309 + 0.616i
           1.23 + 0.254i          0.334 + 0.176i           0.161 + 0.13i
\end{verbatim}

See also: Page~\pageref{fn:acos} \verb+acos()+,
Page~\pageref{fn:asinh} \verb+asinh()+,
Page~\pageref{fn:atan} \verb+atan()+,
Page~\pageref{fn:atan2} \verb+atan2()+,
Page~\pageref{fn:sin} \verb+sin()+.

\newpage 




