Answer
$120^{o}$
Work Step by Step
Solve for radians, then convert to degrees.
$y=\cot^{-1}x$
Domain: $(-\infty, \infty) $
Range: $(0, \pi)$
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$y$ is the number from $(0, \pi)$
such that $\displaystyle \cot y=-\frac{\sqrt{3}}{3}$
In quadrant I, $\displaystyle \cot(\frac{\pi}{3})=\frac{\sqrt{3}}{3}$,
in quadrant II, $\displaystyle \cot(\frac{2\pi}{3})=-\frac{\sqrt{3}}{3}$
$\cot$($\displaystyle \frac{2\pi}{3})=-\sqrt{3}\quad$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 $\displaystyle \frac{180^{o}}{\pi}$
$\displaystyle \theta=\frac{2\pi}{3}\cdot\frac{180^{o}}{\pi}=120^{o}$
