Answer
$y=\displaystyle \frac{3\pi}{4}$
Work Step by Step
$y=\cot^{-1}x$
Domain: $(-\infty, \infty) $
Range: $(0, \pi)$
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$y$ is the number from $(0, \pi)$
such that $\cot y=-1.$
With $\displaystyle \frac{\pi}{4}$ as reference angle, $\displaystyle \cot(\frac{\pi}{4})=1$,
in quadrant II,
$\cot$($\displaystyle \frac{3\pi}{4})=-1\quad$and$\displaystyle \quad \frac{3\pi}{4}\in(0, \pi)$
so
$y=\displaystyle \frac{3\pi}{4}.$
