Answer
$y=\displaystyle \frac{3\pi}{4}$
Work Step by Step
By definition of arccos,
y is the number from $[0, \pi]$ such that $\displaystyle \cos y=-\frac{\sqrt{2}}{2}.$
Using the unit circle,
$\displaystyle \cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}$,
and $\displaystyle \frac{3\pi}{4}\in[0, \pi] ,$
so $y=\displaystyle \frac{3\pi}{4}$
