$x=-\frac{\sin(y)+1}{\cos(y)}$
$x=-\frac{\sin(y)-1}{\cos(y)}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi n_{1}}{2}\text{ and }y<\frac{\pi n_{1}}{2}+\frac{\pi }{2}\right)\text{, }not(n_{1}<-1)\text{ and }not(n_{1}>0)$

$y=\arctan(\frac{-x+\frac{1}{x}}{2})$
$x\neq 0\text{ and }|x|\neq 1$