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: 31


We fill in the blank with $\tan$.

Work Step by Step

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