What is the value of cos(3π/2) - csc(π/2)?

To find the value of cos(3π/2) - csc(π/2), we start by calculating each of the trigonometric functions involved.

First, let's determine cos(3π/2). The angle 3π/2 corresponds to 270 degrees, which is located on the negative y-axis on the unit circle. The cosine of an angle represents the x-coordinate of the point on the unit circle corresponding to that angle. At 3π/2 (or 270 degrees), the coordinates are (0, -1). Therefore, cos(3π/2) is 0.

Next, we calculate csc(π/2). The cosecant function is the reciprocal of the sine function. The angle π/2 corresponds to 90 degrees, where the sine function reaches its maximum value of 1. Thus, csc(π/2) is equal to 1/1, which is also 1.

Now we can substitute these values back into the original expression:

cos(3π/2) - csc(π/2) = 0 - 1 = -1.

This evaluates to -1, making the correct value for the expression cos(3π/2