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: 42

Answer

$\dfrac{\pi}{4}$

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: $2\pi-\theta$ $\frac{5\pi}{4}$ is in Quadrant III. Thus, using formula (3) above gives: reference angle of $\frac{5\pi}{4}$ is $\dfrac{5\pi}{4} - \pi=\dfrac{5\pi}{4}-\dfrac{4\pi}{4} = \dfrac{\pi}{4}$
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