Trigonometry (11th Edition) Clone

Published by Pearson

Chapter 3 - Test - Page 138: 10

Answer

$\cos{(-\frac{7\pi}{6})} = -\frac{\sqrt3}{2}$

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) $\frac{\pi}{6}$ is a special angle whose cosine value is known to be $\frac{\sqrt3}{2}$. Note that the reference angle of $-\frac{7\pi}{6}$ is $\frac{\pi}{6}$. However, since $-\frac{7\pi}{6}$ is in Quadrant II, then its cosine value is negative. Therefore, $\cos{(-\frac{7\pi}{6})} = -\frac{\sqrt3}{2}$

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