Probability distribution function with arctan

[aus_fas]

Hi I have a function \phi =arctan(Y/X) where, X\sim \mathcal{N}(A\cos \theta, v) and Y\sim \mathcal{N}(A\sin \theta,v). I want to find
pdf (probability distribution) of \phi. Any suggestions ? I think change of variables in integral might work??

 

[rochfor1]

There's a change of variables formula for two r.v.s for situations like this. It amounts to changing variables in the integral of the joint pdf.

 

[aus_fas]

There's a change of variables formula for two r.v.s for situations like this. It amounts to changing variables in the integral of the joint pdf.

Thanks,