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: 115


a)$-2$ b)$6$

Work Step by Step

a) I know that $\tan$ is an odd function, which means $f(-\theta)=-f(\theta).$ Therefore $f(-a)=\tan{(-a)}=-\tan{a}=-2$. b) I know that $\tan$ has a period of $\pi$, hence $\tan{\theta}=\tan{(\theta+k\pi)}$ where $k$ is an integer. Thus $f(a)+f(a+\pi)+f(a+2\pi)=\tan{(a)}+\tan{(a+\pi)}+\tan{(a+2\pi)}=\tan{(a)}+\tan{(a)}+\tan{(a)}=2+2+2=6$
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