#### Answer

$y =\displaystyle \frac{2\pi}{3}$

#### Work Step by Step

$y=\cos^{-1}x =\arccos x$
Domain:$[-1, 1] $
Range: $[0, \pi]$
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$y$ is the number from $[0, \pi]$
such that $\displaystyle \cos y=-\frac{\sqrt{3}}{2}.$
Taking $\displaystyle \frac{\pi}{3}$ as a reference angle,$ \displaystyle \cos\frac{\pi}{3}=\frac{1}{2}$,
we have (in quadrant II)
$\displaystyle \cos(\frac{2\pi}{3})=-\frac{1}{2}\qquad$and$\displaystyle \quad \frac{2\pi}{3}\in [0, \pi]$ ,
so
$y =\displaystyle \frac{2\pi}{3}$