Question

What is the number of cycles of y=1/8cos(5θ+π/6)+3 between 0 and 2π?

Answer 1

You are correct. The answer is B) 5.

This is because the period here is T = 2pi/5

Multiplying 5 with this period leads to 5*(2pi/5) = 2pi; showing that 5 full cycles occupy a total horizontal width of 2pi units (more specifically stretching from 0 to 2pi).