# Fourier transform of a cosine function

I was reviewing a homework problem, and I'm trying to figure this out.

The Fourier transform of ${1\over 2} cos(3\pi t)$, according to the solution I was given is ${1\over 2}\{\delta(f+{2\over 3})+\delta(f-{2\over 3})\}$. Wolfram Alpha, however, gives $\sqrt{\pi\over2} \delta(f-3 \pi)+\sqrt{\pi\over2} \delta(f+3 \pi)$. Is the solution I was given the correct one? I don't think Alpha is using $\omega$ (angular frequency, equal to $2\pi f$) in the calculation. That might be where I'm getting confused here.