Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.2 - Radians and Degrees - 3.2 Problem Set - Page 133: 58



Work Step by Step

$\dfrac{5\pi}{3}$ is an angle in Quadrant IV. The reference angle of an angle in Quadrant IV can be found using the formula $2\pi-\theta$. Thus, the reference angle of $\dfrac{5\pi}{3}$ is: $2\pi - \dfrac{5\pi}{3}=\dfrac{6\pi}{3}- \dfrac{5\pi}{3} = \dfrac{\pi}{3}$ $\dfrac{\pi}{3}$ is a special angle whose cosine value is $\dfrac{1}{2}$. $\dfrac{5\pi}{3}$ is in Quadrant IV where cosine is positive. Thus, $\cos{(\frac{5\pi}{3})}=\frac{1}{2}$
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