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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?

enter image description here

user-2147482637
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    It saves writing and makes the equations more clear. Also, the exact values of $\theta$ and $\beta$ aren't known, so writing the exact values isn't an option. – littleO Feb 07 '14 at 00:11
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    @littleO Exactly. The authors might have written "Specifically, $\theta$ and $\beta$ were estimated to be 28.4..." In this context $\theta$ and $\beta$ are estimates, whereas in equations (5) and (7), $\theta$ and $\beta$ refer to the true, unknown values. – TooTone Feb 07 '14 at 00:14
  • My confusion thought is that theta and beta are the actual values they found through the examination of 25 hips, and those are the values that should always be used (since this paper is for motion capture). I guess your saying that theta and beta could be found again for a specific person, but this formula was supposed to be a generalization, which uses those two values – user-2147482637 Feb 07 '14 at 00:19
  • So you would prefer to express the circumference of a circle as $2 * 3.14159265... * r$? – Paul Siegel Feb 07 '14 at 15:30

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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.

Geoff Pointer
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  • thats a great example, thank you – user-2147482637 Feb 07 '14 at 00:23
  • It may sound like reputation hunting, but you're allowed to up vote the question if it helped, as well as accepting it as an answer. I'd also be happy to add to my question if you think it needs more explanation. I'm not sure I've made the point well about the distinction between a well established value of a fundamental concept like $c$ and one that is based on statistical variability in some population. – Geoff Pointer Feb 07 '14 at 00:29
  • @Geoff Pointer it's a good point but I think the OP needs 15 Rep? Someone else needs to upvote the question! – TooTone Feb 07 '14 at 00:39
  • @TooTone Good point, that was so far back I forgot. I will be posting a report on meta though, because the help page forgets to say an initial privilege is accepting questions. – Geoff Pointer Feb 07 '14 at 00:42
  • @GeoffPointer (it's quite counter-intuitive) – TooTone Feb 07 '14 at 00:45
  • Yes i tried upvoting (i frequent stack overflow, first time on math version) but i dont have enough reputation. It would be nice if stackexchange would keep reputation from different sister sites – user-2147482637 Feb 07 '14 at 00:56
  • @user1938107 You get an automatic +100 if you have over 200 at a sister site. – Geoff Pointer Feb 07 '14 at 01:29
  • ah, im only at 135 :( – user-2147482637 Feb 07 '14 at 02:28
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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 $e$).

vonbrand
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