Final answer:
The value of the trigonometric function cot 5π/2 is undefined.
Step-by-step explanation:
The given trigonometric function is cot 5π/2. In order to find the value of this function, we need to evaluate the cotangent of 5π/2. The cotangent function is the reciprocal of the tangent function, so we can rewrite the expression as 1/tan 5π/2.
The tangent function has a period of π, so we can find an equivalent angle within one period. 5π/2 is already within the first period, so we don't need to make any adjustments.
The tangent function is undefined when the angle is equal to (2n+1)π/2, where n is an integer. Since 5π/2 is equal to (2*2+1)π/2, the tangent function is undefined at this angle. Therefore, the cotangent of 5π/2 is also undefined.