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 218: 22


The answer to this exercise is $$\cos\frac{\pi}{10}$$

Work Step by Step

$$\sin\frac{2\pi}{5}$$ First, cosine is the cofunction of sine. We now need to find the complementary angle $\theta$ for cosine, which satisfies $$\cos\theta=\sin\frac{2\pi}{5}\hspace{1cm}(1)$$ According to Cofunction Identity: $\cos\theta=\sin(\frac{\pi}{2}-\theta)$ Apply this to the equation $(1)$: $$\sin(\frac{\pi}{2}-\theta)=\sin\frac{2\pi}{5}$$ $$\frac{\pi}{2}-\theta=\frac{2\pi}{5}$$ $$\theta=\frac{\pi}{2}-\frac{2\pi}{5}=\frac{\pi}{10}$$ Therefore $\cos\frac{\pi}{10}$ is the answer.
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