Evaluate the following without a calculator. csc(-(5pi )/(2)) Select the correct choice below and, if necessary fill in the answer box to complete your choice. A. csc(-(5pi )/(2))=square (Simplify your answer.) B. The expression is undefined

To evaluate \( \csc\left(-\frac{5\pi}{2}\right) \) without a calculator, we need to understand the properties of the cosecant function and the angle involved.First, let's recall that the cosecant function is the reciprocal of the sine function: Next, we need to find the sine of the angle .The angle can be converted to a positive angle by adding (since adding to an angle results in a coterminal angle): So, \( \sin\left(-\frac{5\pi}{2}\right) = \sin\left(-\frac{\pi}{2}\right) \).We know that: Now, we can find the cosecant: Therefore, the correct choice is:A. \( \csc\left(-\frac{5\pi}{2}\right) = -1 \)