Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 496: 2



Work Step by Step

We know that $\sin$, $\csc$, and $\tan$ are odd trigonometric functions. This implies that $f(-\theta)=-f(\theta)$ So, $\sin(-\theta)=-\sin(\theta)$ We also know that $\cos$, $\sec$ are even trigonometric functions. This implies that $f(-\theta)=f(\theta)$ So, $\cos(-\theta)=\cos(\theta).$ Thus, $\sin(-\theta)+\cos(-\theta)=-\sin(\theta)+\cos(\theta) =\cos(\theta) -\sin (\theta) $ Therefore, the given statement is True.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.