Question

$$q=\cos\ x$$

Solve for q

$q=\cos(x)$

Solve for x

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