Answer
$\frac{3\pi}{4}$
Work Step by Step
$\cos^{-1}(-\frac{\sqrt 2}{2})= \cos^{-1}(-\frac{1}{\sqrt 2})$.
Let $\cos^{-1}(-\frac{1}{\sqrt 2})=y$. Then,
cos y= $-\frac{1}{\sqrt 2}= -cos(\frac{\pi}{4})= \cos(\pi-\frac{\pi}{4})= \cos \frac{3\pi}{4}$.
Therefore, y= $\frac{3\pi}{4}$.
