Answer
$y =\displaystyle \frac{\pi}{4}$
Work Step by Step
$y=\sin^{-1}x =\arcsin x$
Domain: $[-1, 1] $
Range: $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$
-----------
$y$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$
such that $\displaystyle \sin y=\frac{\sqrt{2}}{2}.$
$\displaystyle \sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\qquad$and$\displaystyle \quad \frac{\pi}{4}\in[-\frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$,
so
$y =\displaystyle \frac{\pi}{4}$
