COMC 2017 C Problem 2

A function f(x) is periodic with period T>0 if f(x+T)=f(x) for all x. The smallest such number T is called the least period. For example, the functions \sin (x) and \cos (x) are periodic with least period 2 \pi.

(a) Let a function g(x) be periodic with the least period T=\pi. Determine the least period of g(x / 3).
(b) Determine the least period of H(x)=\sin (8 x)+\cos (4 x).
(c) Determine the least periods of each of G(x)=\sin (\cos (x)) and F(x)=\cos (\sin (x)).