Question

$$y = \sin x$$

Solve for x

$x=-\arcsin(y)+2\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}$
$x=\arcsin(y)+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 1$

Solve for y

$y=\sin(x)$