Evaluate the following without a calculator. csc(-(3pi )/(2)) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. D A. csc(-(3pi )/(2))=square (Simplify your answer.) B. The expression is undefined.

To evaluate \( \csc\left(-\frac{3\pi}{2}\right) \) without a calculator, we need to understand the properties of the cosecant function and the unit circle.The cosecant function is defined as: First, let's find the angle on the unit circle. This angle is equivalent to rotating radians clockwise from the positive x-axis. The angle radians corresponds to 270 degrees, which points to the negative y-axis. Therefore, radians also points to the negative y-axis.Next, we need to determine the sine of : Now, we can find the cosecant: So, the correct choice is:A. \( \csc\left(-\frac{3\pi}{2}\right) = -1 \)