Any reason beyond academics to represent a known constant as variable? In biomechanics, for calculating joint angles there is a research paper most often referenced and which most of the algorithms are based on http://www.sciencedirect.com/science/article/pii/016794579190046Z#.  
In the paper, they use sin(beta) and cos(theta), however, they have just defined what theta and beta are, so why are they not used as a sort of coefficient to the formula.  Is there some sort of mathematical reason or standard, or it just looks pretty?

 A: Consider a concept like the speed of light and its value represented by $c$. When writing physics do you want to always write the number $3.00\times10^8$ when $c$ is much more convenient? Also, if all your constants were written as numbers their meaning in context would be much harder to ascertain. It's more about their meaning than their particular values.
With a constant like $c$ there is negligible disagreement about its value. In the case you have mentioned, their meaning remains the same regardless of how many different studies have and will be done and how much disagreement there may turn out to be about their actual value. So, no, it's about much more than just looking pretty.
A: While the values of, say, $\cos \theta$ and others might be fixed, it may be useful to have them in that form to apply trigonometric identities. Besides, the fact that $\theta$ is a specific angle may help in visualizing its relation with other variables. And, last but not least, often a constant is named because its value isn't known precisely (like $c$ for the speed of light), because the exact value is cumbersome ($\pi$ is irrational, even transcendent; no way of giving its exact value ever), or just for mnemonic help (a physicist knows immediately what is being talked about when confronted to $e$).
