Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Review Exercises - Page 285: 52

Answer

$\theta = 30^{\circ}, 150^{\circ}, 270^{\circ}$

Work Step by Step

$sin~\theta-cos~2\theta = 0$ $sin~\theta-(1-2sin^2\theta) = 0$ $2sin^2\theta+sin~\theta-1 = 0$ $(2sin\theta-1)(sin~\theta+1) = 0$ $(2sin\theta-1) = 0$ or $(sin~\theta+1) = 0$ $sin~\theta = \frac{1}{2}$ or $sin~\theta = -1$ $\theta = 30^{\circ}, 150^{\circ}$ or $\theta = 270^{\circ}$
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