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: 117


a)$-4$ b)$(-12)$

Work Step by Step

a) I know that $\sec$ is an even function, which means $f(-\theta)=f(\theta).$ Therefore $f(-a)=\sec{(-a)}=\sec{a}=-4$. b) I know that $\sec$ has a period of $2\pi$, hence $\sec{\theta}=\sec{(\theta+2k\pi)}$ where $k$ is an integer. Thus $f(a)+f(a+2\pi)+f(a+4\pi)=\sec{(a)}+\sec{(a+2\pi)}+\sec{(a+4\pi)}=\sec{(a)}+\sec{(a)}+\sec{(a)}=(-4)+(-4)+(-4)=(-12)$
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