Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \csc \frac{3 \pi}{2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value of \( \csc \frac{3 \pi}{2} \) is B. \( \csc \frac{3 \pi}{2} \) is undefined.

To evaluate \( \csc \frac{3 \pi}{2} \), we start by determining the sine of the angle. The angle \( \frac{3 \pi}{2} \) corresponds to 270 degrees, which is located on the negative y-axis. At this point, the sine value is \( -1 \). Since cosecant is the reciprocal of sine, we have: \[ \csc \frac{3 \pi}{2} = \frac{1}{\sin \frac{3 \pi}{2}} = \frac{1}{-1} = -1. \] So the answer to the expression is A. The value of \( \csc \frac{3 \pi}{2} \) is \( -1 \).