# What is the period of f(t)=cos 8 t ?

The period is $\frac{\pi}{4}$. See explanation.
For any trigonometric function if the variable is multiplied by $a$ then the period is $a$ times smaller.
Here the basic function is $\cos t$, so the basic period is $2 \pi$. The coefficient by which $t$ is multiplied is $8$, so the new period is: