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 - Page 575: 57

Answer

$\dfrac{\pi}{4}$

Work Step by Step

The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps: a) Quadrant- I: $\theta $ b) Quadrant -II: $(\pi-\theta)$ c) Quadrant- III: $(\theta - \pi)$ d) Quadrant - IV: $(2\pi - \theta)$ We can see that the angle $\dfrac{11\pi}{4}$ is close to $\dfrac{12\pi}{4}=3\pi $. Thus, the reference angle of $\dfrac{11\pi}{4}$ is: $ = 3\pi - \dfrac{11\pi}{4} $ $\implies =\dfrac{12\pi}{4} - \dfrac{11\pi}{4}$ $ =\dfrac{\pi}{4}$
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