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: 25


To write $\sin\frac{5\pi}{8}$ in terms of cofunction, $\cos(-\frac{\pi}{8})$ would be the answer.

Work Step by Step

$$\sin\frac{5\pi}{8}$$ As cosine and sine are cofunctions, in order to write $\sin\frac{5\pi}{8}$ in terms of cofunction, we now need to find $\theta$, which must satisfy $$\cos\theta=\sin\frac{5\pi}{8}\hspace{1cm}(1)$$ According to Cofunction Identity: $\cos\theta=\sin(\frac{\pi}{2}-\theta)$ Apply this to the equation $(1)$: $$\sin(\frac{\pi}{2}-\theta)=\sin(\frac{5\pi}{8})$$ $$\frac{\pi}{2}-\theta=\frac{5\pi}{8}$$ $$\theta=\frac{\pi}{2}-\frac{5\pi}{8}=-\frac{\pi}{8}$$ $\cos(-\frac{\pi}{8})$ is the answer to this exercise.
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