Example 1 (continuous periodic function)

$$f(x) = \cos 3x, \qquad x \in {\mathbb{R}}.$$ (4)

$f$ is periodic, and $2\pi$ is a period, however not the smallest one. The period is $p = \displaystyle{\frac{2\pi}{3}}$. Verify that (i) $${\frac{2\pi}{3}}$$ is a period, (ii) $${\frac{2\pi}{3}}$$ is actually the period. For (ii), use the fact that the period os $\cos$ is $2\pi$.