The cosine function has period 2pi. The function f(x)=acoskx (k>0) completes one period as k varies from 0 to 2pi.
So this function complete one period as x varies between 0 and (2pi)/k and thus have period (2pi)/k.
Again, the number |a| is called the amplitude and it is the largest value this particular function can attain.
For the given function `f(x)=1/3cos(4x)` , amplitude is given by |1/3|, i.e. `1/3` and period is `(2pi)/4` , i.e. `pi/2` .