Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Review Exercises - Page 291: 13



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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