$\displaystyle \sin z = \sin c \hfill \\$

$\displaystyle z = x + iy \hfill \\$

$\displaystyle c = a + ib \hfill \\$

$\displaystyle a,b,x,y \in \mathbb{R} \hfill \\$

$\displaystyle {\text{seperating the real and imaginary part I have the following system to solve}} \hfill \\$

$\displaystyle \left\{ \begin{gathered}

\sin x\cosh y = \sin a\cosh b \hfill \\

\cos x\sinh y = \cos a\sinh b \hfill \\

\end{gathered} \right. \hfill \\ $

But I don't see how I can solve this. Any idea?