Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Test - Page 138: 12



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, $\sec{(\frac{8\pi}{3})} = \dfrac{1}{-\frac{1}{2}}=-2$
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