Fourier Transformation, calculus computations

Hi! I hope this is the right place to post this :)

I need to compute the Fourier transform of f(x,y) = sin(x) sin(y). I know that there's the hard way and a couple of easy ways to do this and I want to find one of the easy ways instead of actually solving integrals. I've looked on the internet and there are lots of examples of doing it the long way, but nothing jumped out at me as being easier. I want to find the easier way because I also need to find the Fourier Transform of f(t) = cos(16 pi t) cos(64 pi t), which I'm totally lost on. I know that 16 is 1/4 of 64, which will push the frequencies further apart. I (think atlease) can draw the output, but for actually solving, I'm not quite sure what to do.

Any help would be excellent!