# How do you determine the period for f(x) = 3 cos (2/3)x?

I think that your fnction is $f \left(x\right) = 3 \cos \left(\frac{2}{3} x\right)$.
You can find the period by considering the number in front of $x$, i.e., $\frac{2}{3}$, that you can call $k$.
$k = \frac{2 \pi}{p e r i o d}$
$p e r i o d = 3 \pi$