Answer
$120^{o}$
Work Step by Step
Solve for radians, then convert to degrees.
$y=\cos^{-1}x =\arccos x$
Domain:$[-1, 1] $
Range: $[0, \pi]$
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$y$ is the number from $[0, \pi]$
such that $\displaystyle \cos y=-\frac{1}{2}.$
In quadrant I, , $\displaystyle \cos\frac{\pi}{3}=\frac{1}{2}$,
In quadrant II,
$\displaystyle \cos(\frac{2\pi}{3})=-\frac{1}{2}\qquad$and$\displaystyle \quad \frac{2\pi}{3}\in [0, \pi]$ ,
so
$y =\displaystyle \frac{2\pi}{3}$
To convert radians to degrees, multiply y with $\displaystyle \frac{180^{o}}{\pi}$
$\displaystyle \theta=\frac{2\pi}{3}\cdot\frac{180^{o}}{\pi}=120^{o}$
