Question

How do you find the period of $$y = \cos (2x) $$ ?

Answer 1

Period = $$ \pi $$
Explanation :
If we express the cosine function in the following way :
$$y = a \cos (bx + c) + d $$
Then:
$$|a| $$ = the amplitude
$$\dfrac{2 \pi}{|b|} $$ = the period
$$ \dfrac{-c}{b} $$ = the phase shift
$$d$$ = the vertical shift
For given function we have :
$$|b| = 2 $$
So period is :
$$ \dfrac{2 \pi}{2} = \pi $$
The graph confirms this: