# How do you evaluate sin^-1(-1/sqrt2)?

$- \frac{\pi}{4}$
Let ${\sin}^{-} 1 \left(- \frac{1}{\sqrt{2}}\right) = \theta .$
Then, by defn. of ${\sin}^{-} 1 , \sin \theta = - \frac{1}{\sqrt{2}}$, where, $\theta \in \left[- \frac{\pi}{2} , \frac{\pi}{2}\right]$
We have, $\sin \left(- \frac{\pi}{4}\right) = - \frac{1}{\sqrt{2}} ,$ & $- \frac{\pi}{4} \in \left\{- \frac{\pi}{2} , \frac{\pi}{2}\right]$, $\theta = - \frac{\pi}{4}$