The period of a function is the size of the intervals over which the function repeats.
sin(x) and cos(x) have period 2π radians, this is every revolution or complete circle.
tan(x) and cot (x) have period πr adian. They both repeat over intervals of π radian.
When you multiply the argument the period gets divided by that factor.
Then, cot [(π/2)x] has period π radian / (π/2) = 2 radian.
Answer: 2 radians.