The position of a mass that is oscillating on a spring is given by (15.9 cm) because [(2.64 s-1) t].
What is frequency of this motion?

You should know that:

T = \frac{1}{f}

That is periodic time is the reciprocal of frequency.

So, find the periodic time, then take the reciprocal to get the frequency.

Just to be sure, is this your equation?:

15.9cos[(2.64s-1)t]

Yeah, I was wondering because I have seen

x(t)=Asin({\omega}t-{\phi})

where, as you pointed out, T=\frac{2\pi}{\omega}\rightarrow f=\frac{1}{T}=\frac{\omega}{2\pi}