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: 21


$\sin\frac{5\pi}{12}$ is the cofunction of $\cos\frac{\pi}{12}$.

Work Step by Step

$$\cos\frac{\pi}{12}$$ First, sine is the cofunction of cosine. Therefore, we now need to find the complementary angle $\theta$ for sine, which satisfies $$\sin\theta=\cos\frac{\pi}{12}\hspace{1cm}(1)$$ According to Cofunction Identity: $\sin\theta=\cos(\frac{\pi}{2}-\theta)$ Apply this to the equation $(1)$: $$\cos(\frac{\pi}{2}-\theta)=\cos\frac{\pi}{12}$$ $$\frac{\pi}{2}-\theta=\frac{\pi}{12}$$ $$\theta=\frac{\pi}{2}-\frac{\pi}{12}=\frac{5\pi}{12}$$ Therefore $\sin\frac{5\pi}{12}$ is the answer.
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