Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set: 44

Answer

$\dfrac{2\pi}{7}$

Work Step by Step

RECALL: The following are the means on how to find the reference angle of an angle $\theta$ based on its position: (1) Quadrant I: $\theta$ (itself) (2) Quadrant II: $\pi-\theta$ (3) Quadrant III: $\theta - \pi$ (4) Quadrant IV: $2\pi-\theta$ $\dfrac{5\pi}{7}$ is in Quadrant II. Thus, using formula (2) above gives: reference angle of $\dfrac{5\pi}{7}$ is $\pi - \dfrac{5\pi}{7}=\dfrac{7\pi}{7}-\dfrac{5\pi}{7} = \dfrac{2\pi}{7}$
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