Answer
$\frac{3\pi}{4}.$
Work Step by Step
Since $\cot\left(-\frac{\pi}{4} \right)=-1$, we have
$$\cot^{-1}\left(\cot\left(-\pi \right)\right)=\cot^{-1}\left(-1\right)=\frac{3\pi}{4}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 374: 16
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