1. **State the problem:** Given $\sin(t) = \frac{3}{8}$, find (a) $\sin(-t)$ and (b) $\csc(-t)$. 2. **Recall important trigonometric identities:** - $\sin(-x) = -\sin(x)$ (sine is an odd function). - $\csc(x) = \frac{1}{\sin(x)}$. - $\csc(-x) = \frac{1}{\sin(-x)}$. 3. **Calculate (a) $\sin(-t)$:** Using the odd function property, $$\sin(-t) = -\sin(t) = -\frac{3}{8}.$$ 4. **Calculate (b) $\csc(-t)$:** First, find $\sin(-t)$ from step 3, then $$\csc(-t) = \frac{1}{\sin(-t)} = \frac{1}{-\frac{3}{8}} = -\frac{8}{3}.$$ **Final answers:** (a) $\sin(-t) = -\frac{3}{8}$ (b) $\csc(-t) = -\frac{8}{3}$