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: 41



Work Step by Step

$$\sin(3\theta-15^\circ)=\cos(\theta+25^\circ)\hspace{1cm}(1)$$ Cofunction identity: $$\cos\theta=\sin(90^\circ-\theta)$$ So, $$\cos(\theta+25^\circ)=\sin[90^\circ-(\theta+25^\circ)]$$ $$\cos(\theta+25^\circ)=\sin(65^\circ-\theta)$$ Replace this in $(1)$ for $\cos(\theta+25^\circ)$: $$\sin(3\theta-15^\circ)=\sin(65^\circ-\theta)$$ $$3\theta-15^\circ=65^\circ-\theta$$ $$4\theta=80^\circ$$ $$\theta=20^\circ$$
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