Answer
$$y=-\frac{\pi}{4}$$
Work Step by Step
$$y=\sin^{-1}(-\frac{\sqrt2}{2})$$
*Remember: $\sin^{-1}A=x$ means that $\sin x=A$
Therefore, to find $y$, we need to recall which value of $y$ would have $\sin y=-\frac{\sqrt2}{2}$.
$\sin y\lt0$ shows that we can find a value of $y$ in either quadrant III or IV of the unit circle. The choice is arbitrary. I would choose quadrant IV here.
In quadrant IV, $-\frac{\pi}{4}$ is the value of the angle with which $\sin(-\frac{\pi}{4})=-\frac{\sqrt2}{2}$
Therefore, $$y=-\frac{\pi}{4}$$
