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: 35

Answer

$\csc$ needs to be filled in the blank.

Work Step by Step

$$\cos70^\circ=\frac{1}{A20^\circ}\hspace{1cm}(1)$$ From the Cofunction Identity: $$\cos\theta=\sin(90^\circ-\theta)$$ So $$\cos70^\circ=\sin(90^\circ-70^\circ)=\sin20^\circ$$ Also, from Reciprocal Identity: $$\sin\theta=\frac{1}{\csc\theta}$$ Therefore, $$\cos70^\circ=\frac{1}{\csc20^\circ}$$ We thus need to fill in the blank with $\csc$.
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