Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 200: 22

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

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