hard to solve 2D integral

Question

I want to calculate the following integral: $$ \int_\mathbb{R^2}\frac{\sin(ak)}{k}e^{i\vec{k}\vec{r}}d^2k $$ and my idea was to do a transformation into polar coordinates. with $d^2k=k\,d\phi\, dk$ I get $$ \int_0^\infty\int_0^{2\pi}\sin(ak)e^{ikr\cos(\phi) }\,d\phi\, dk $$ but then I don't know how to deal with this term. I know that if it was 3D, I could make a transformation into spherical coordinates and substitute $\cos(\phi)=z$ and it would work. but in 2d I can't do that because I don't get a $\sin(\phi)$ from the differential that I'd get from spherical coordinates. My idea now is to still somehow make a transformation into spherical coordinates although it is 2D. Could I do that? or is there another way to solve this integral?