Transformation of functions: proof for the time period

Question

Given the standard form of a trigonometric function: $a \times \cos(b(t+c)) + d$, what is the proof that the period $p = \frac{2 \times \pi}{b}$.

We don't have the proof in our syllabus. I'm just asking out of curiosity.

Answer 1

This isn't a formal proof, but just an informal argument.

Suppose that $b(t_1+c)=0$ and $b(t_2+c)=2\pi$.

What is $t_2-t_1$?