1. **State the problem:** Determine if the statements \(\sin \theta > 0\) and \(\csc \theta < 0\) are possible or impossible. 2. **Recall definitions and relationships:** - \(\sin \theta\) is the sine of angle \(\theta\). - \(\csc \theta = \frac{1}{\sin \theta}\) is the cosecant of \(\theta\). 3. **Analyze the first statement:** \(\sin \theta > 0\) means sine is positive. - Sine is positive in the first and second quadrants. 4. **Analyze the second statement:** \(\csc \theta < 0\) means cosecant is negative. - Since \(\csc \theta = \frac{1}{\sin \theta}\), the sign of \(\csc \theta\) matches the sign of \(\sin \theta\). - If \(\sin \theta > 0\), then \(\csc \theta = \frac{1}{\sin \theta} > 0\). 5. **Conclusion:** - The statements \(\sin \theta > 0\) and \(\csc \theta < 0\) cannot both be true simultaneously. - Therefore, the combined statement is **impossible**. **Final answer:** The statements \(\sin \theta > 0\) and \(\csc \theta < 0\) together are impossible.