Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Review Exercises - Page 285: 13

Answer

$y=\frac{-\pi}{4}$

Work Step by Step

RECALL: $y=\text{arccot}{(x)} \longrightarrow \tan{y}=\frac{1}{x}$, $y$ is in the interval $(-\frac{\pi}{2}, \frac{\pi}{2})$ Thus, $y=\text{arccot}{(-1)}$ implies that $\tan{y}=\frac{1}{-1}=-1$. Note that $\tan{(\frac{\pi}{4})}=1$. Since tangent is an odd function, then $\tan{(-x)} = -\tan{x}$. This means that $\tan{(-\frac{\pi}{4})}=-\tan{(\frac{\pi}{4})}=-1$. Therefore, $y=\text{arccot}(-1)\longrightarrow y=\frac{-\pi}{4}$
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