Question

Find the fundamental period of f when
f(x) = 2 cos(9x) .

Answer 1

What is the period of cos x?

Answer 2

pi

Answer 3

Given that, if we write T for the period of your function, for what value of T is
f(t+T) = f(t)
i.e.,
2cos(9(t+T)) = 2cos(9t)
i.e.,
cos(9t + 9T) = cos(9t)

It must be that 9T = 2pi

Hence the period of your function f, is T = 2pi/9.

Answer 4

The period of cos x and sin x is 2pi. That is why we set 9T = 2pi.