Question

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

Answer 1

I think that your fnction is `f(x)=3cos(2/3x)`.
You can find the period by considering the number in front of `x`, i.e., `2/3`, that you can call `k`.

`k=(2pi)/(period)`

So:
`period=3pi`

Graphically: