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: 36


We need to fill in the blank with $\tan$.

Work Step by Step

$$\tan24^\circ=\frac{1}{A66^\circ}\hspace{1cm}(1)$$ From the Cofunction Identity: $$\tan\theta=\cot(90^\circ-\theta)$$ So $$\tan24^\circ=\cot(90^\circ-24^\circ)=\cot66^\circ$$ Also, from Reciprocal Identity: $$\cot\theta=\frac{1}{\tan\theta}$$ Therefore, $$\tan24^\circ=\frac{1}{\tan66^\circ}$$ We thus need to fill in the blank with $\tan$.
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