Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 219: 38



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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