I'll start with a general description and then supply my specific case. I've got data that is generated via the product of $f$ and $g$, i.e. $fg$. Both of these have distributions, and as such the product is also a distribution. I'd like to write down a probability distribution function that describes this (so I can then fit the data).
Now for the case-scenario, in a hope to clarify what I seek. My data follows $D = P \cos(\theta)$, where $P$ is a distribution of momenta and $\theta$ is a distribution of angles such that $\cos(\theta)$ is a uniform distribution. This can be seen here: 
$\cos(\theta)$" />
The distribution of momenta appears to be exponential in simplest approximation, but maybe more-so like a beta distribution. It looks like this:
$P$" />
The actual data is generate by the product of these sets, and when binned looks like the following:
$D = P \cos(\theta)$" />
To summarize, I can write an approximate PDF for $P$ in the domain of energy, and would like to do the same for $D$, but don't know how to mix in the angular component. If a convolution is necessary, I don't see how to perform it because the PDF I'd write for the angular component wouldn't be in the same domain (Energy) as the momenta $P$.
To try and frame my question with the correct terminology, given a PDF of $f(x)$ and random variable $U$, how can I write the composite PDF $h(x)=f(x)\,U$?