# What is the period of f(t)=cos ( ( 3 t ) / 2 ) ?

##### 1 Answer
Dec 18, 2015

$\frac{4 \pi}{3}$

#### Explanation:

The period of $\cos \left(x\right)$ is $2 \pi$, thus to find the period, we solve the equation

$\frac{3 t}{2} = 2 \pi$

$\implies 3 t = 4 \pi$

$\implies t = \frac{4 \pi}{3}$

So $\frac{3 t}{2}$ increases by $2 \pi$ when $t$ increases by $\frac{4 \pi}{3}$, meaning $\frac{4 \pi}{3}$ is the period of $f \left(t\right)$.