QuestionFind the sign of $\csc \left(\theta+180^{\circ}\right)$ for $90^{\circ}<\theta<180^{\circ}$.

Studdy Solution
This means that $\theta+180^{\circ}$ is in the fourth quadrant. As we established earlier, the sine (and therefore the cosecant) function is negative in the fourth quadrant.
Therefore, $\csc \left(\theta+180^{\circ}\right)$ is negative.