1. **Stating the problem:** We want to find the intervals where $\sin(x) > 0$ and $\csc(x) < 0$. 2. **Recall definitions and relationships:** - $\sin(x)$ is the sine function. - $\csc(x) = \frac{1}{\sin(x)}$ is the cosecant function. 3. **Analyze the inequalities:** - $\sin(x) > 0$ means sine is positive. - $\csc(x) < 0$ means cosecant is negative. 4. **Important rule:** Since $\csc(x) = \frac{1}{\sin(x)}$, the sign of $\csc(x)$ depends on the sign of $\sin(x)$. 5. **Sign relationship:** - If $\sin(x) > 0$, then $\csc(x) = \frac{1}{\sin(x)} > 0$. - If $\sin(x) < 0$, then $\csc(x) < 0$. 6. **Conclusion:** The conditions $\sin(x) > 0$ and $\csc(x) < 0$ cannot be true simultaneously because they contradict each other. **Final answer:** There is no $x$ such that $\sin(x) > 0$ and $\csc(x) < 0$ at the same time.