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

$\pi$
The period of $\cos \left(x\right)$ is $2 \pi$, thus the period of $\cos \left(2 t\right)$ is the change needed in $t$ for $2 t$ to change by $2 \pi$. So
$2 t = 2 \pi \implies t = \pi$.
Thus the period is $\pi$.