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: 60



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 $\dfrac{13\pi}{3}$ is close to $\dfrac{12\pi}{3}=4\pi $. Thus, the reference angle of $\dfrac{13\pi}{3}$ is: Thus, the reference angle is: $ = \dfrac{13 \pi}{ 3} -4\pi $ $\implies =\dfrac{13 \pi}{3} - \dfrac{12 \pi}{3}$ $ =\dfrac{\pi}{3}$
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