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: 114


a)$\frac{1}{4}$ b)$\frac{3}{4}$

Work Step by Step

a) I know that $\cos$ is an even function, which means $f(-\theta)=f(\theta).$ Therefore $f(-a)=\cos{(-a)}=\cos{a}=\frac{1}{4}$. b) I know that $\cos$ has a period of $2\pi$, hence $\cos{\theta}=\cos{(\theta+2k\pi)}$ where $k$ is an integer. Thus $f(a)+f(a+2\pi)+f(a-2\pi)=\cos{(a)}+\cos{(a+2\pi)}+\cos{(a-2\pi)}=\cos{(a)}+\cos{(a)}+\cos{(a)}=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}$
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