Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.3 Properties of the Trigonometric Functions - 6.3 Assess Your Understanding - Page 395: 116


a) $3$ b)$-9$

Work Step by Step

a) I know that $\cot$ is an odd function, which means $f(-\theta)=-f(\theta).$ Therefore $f(-a)=\cot{(-a)}=-\cot{a}=3$. b) I know that $\cot$ has a period of $\pi$, hence $\cot{\theta}=\cot{(\theta+k\pi)}$ where $k$ is an integer. Thus $f(a)+f(a+\pi)+f(a+4\pi)=\cot{(a)}+\cot{(a+\pi)}+\cot{(a+4\pi)}=\cot{(a)}+\cot{(a)}+\cot{(a)}=(-3)+(-3)+(-3)=(-9)$
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