How do you evaluate sin^-1(-sqrt(2)/2)?

It is $- \frac{\pi}{4}$
${\sin}^{-} 1 \left(- \frac{\sqrt{2}}{2}\right) = {\sin}^{-} 1 \left(\sin \left(- \frac{\pi}{4}\right)\right) = - \frac{\pi}{4}$