Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 194: 18

Answer

$$\sin\theta=-\frac{5}{8}$$

Work Step by Step

$$\csc\theta=-\frac{8}{5}$$ We have the following identity $$\csc\theta=\frac{1}{\sin\theta}\hspace{1cm}\text{(Reciprocal Identities)}$$ so, $$\sin\theta=\frac{1}{\csc\theta}$$ $$\sin\theta=\frac{1}{-\frac{8}{5}}=-\frac{5}{8}$$
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