Trigonometry (10th Edition)

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

Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 213: 38

Answer

$$\theta=20^\circ$$

Work Step by Step

$$\sin\theta=\cos(2\theta+30^\circ)\hspace{1cm}(1)$$ - Identity of the cofunction: $$\sin\theta=\cos(90^\circ-\theta)$$ Replace into $(1)$: $$\cos(90^\circ-\theta)=\cos(2\theta+30^\circ)$$ $$90^\circ-\theta=2\theta+30^\circ$$ $$3\theta=60^\circ$$ $$\theta=20^\circ$$
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