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: 32


We fill in the blank with $\cos$.

Work Step by Step

$$\sin\frac{2\pi}{3}=A\Big(-\frac{\pi}{6}\Big)\hspace{1cm}(1)$$ We notice that $$\frac{2\pi}{3}+\Big(-\frac{\pi}{6}\Big)=\frac{4\pi-\pi}{6}=\frac{3\pi}{6}=\frac{\pi}{2}$$ That means we can rewrite $(1)$ as $$\sin\frac{2\pi}{3}=A\Big(\frac{\pi}{2}-\frac{2\pi}{3}\Big)$$ Now from the Cofunction Identity: $$\sin\theta=\cos(\frac{\pi}{2}-\theta)$$ So $$A=\cos$$ In other words, we fill in the blank with $\cos$.
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