# How do you find the period of y=3+ cos x?

May 8, 2016

$2 \pi$

#### Explanation:

The period of f(x) = a + b cos (cx + d) is $\frac{2 \pi}{c}$

$f \left(x + p e r i o d\right) = f \left(x + \frac{2 \pi}{c}\right) = a + b \cos \left(c \left(x + \frac{2 \pi}{c}\right) + d\right)$

$= a + b \cos \left(\left(c x + d\right) + 2 \pi\right)$

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

$= f \left(x\right)$

Here, c = 1, and so, the period is $2 \pi$..