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


$\csc$ 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 $\csc$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.