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

Apr 11, 2018

$\text{Period} = \pi$

#### Explanation:

If we express the cosine function in the following way:

$y = a \cos \left(b x + c\right) + d$

Then:

$\setminus \setminus \setminus \boldsymbol{|} a | \setminus \setminus \setminus = \text{the amplitude}$

$\boldsymbol{\frac{2 \pi}{|} b |} \setminus \setminus = \text{the period}$

$\boldsymbol{\frac{- c}{b}} = \text{the phase shift}$

$\setminus \setminus \setminus \setminus \boldsymbol{d} \setminus \setminus \setminus = \text{the vertical shift}$

For given function we have:

$| b | = 2$

So period is:

$\frac{2 \pi}{2} = \pi$

The graph confirms this: