Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Test - Page 132: 12

Answer

$-2$

Work Step by Step

Recall: (1) An angle and its reference angle either have the same trigonometric function values or differ only in signs. (2) $\sec{\theta} = \dfrac{1}{\cos{\theta}}$ $\frac{\pi}{3}$ is a special angle whose cosine value is known to be $\frac{1}{2}$. Note that the reference angle of $\frac{8\pi}{3}$ is $\frac{\pi}{3}$. However, since $\frac{8\pi}{3}$ is in Quadrant II, then its cosine value is negative. Therefore, $\sec{(\frac{8\pi}{3})} = \dfrac{1}{-\frac{1}{2}}=-2$
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.