How do I find the Fourier transform of a function that is separable into a radial and an angular part? how do I find the Fourier transform of a function that is separable into a radial and an angular part: 
$f(r, \theta, \phi)=R(r)A(\theta, \phi)$ ?
Thanks in advance for any answers!

You can use the expansion of a plane wave in spherical waves. If you integrate the product of your function with such a plane wave, you get integrals over $R$ times spherical Bessel functions and $A$ times spherical harmonics; you'll need to be able to solve those in order to get the Fourier coefficients.
