Talk:Proofs of trigonometric identities

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The List of Trigonometric Identitites should only show the actual identities, then have external links to a particular identity's proof(s). That way we can save space on the actual page but still be able to access additional information on the identity. Overall this would make the page more organised and concise.

Contents

[edit] To avoid redundancy, let's move all proofs of trigonometric identities from other pages onto this single page.

I've noticed that many articles give trigonometric identities and prove them. But when two or more articles prove the same identity, it is a waste of space (even if they use different proofs). I propose that all proofs of trigonometric identities to be placed on this page, so that there will never be any repetition of proofs. --Ķĩřβȳ♥ŤįɱéØ 10:59, 20 October 2006 (UTC)

Sweet job here man. Good move. ☢ Ҡi∊ff⌇↯ 14:17, 20 October 2006 (UTC)
I like this idea. List of trigonometric identities really needs to be cleaned up, and removing proofs would be a good way to do that. This page might end up getting pretty long, though... after all, many things can be proven in more than one way (e.g. proof of angle sum trig identity via geometric methods or Euler's formula). Whoever is working on this task, I wish you the best of luck in remaining organized and coherent. I will watch this page and help out sporadically. --Qrystal 13:48, 15 November 2006 (UTC)

THIS page in its present form is a horrible horrible mess. List of trigonometric identities, on the other hand, seems reasonable. I think it's reasonable to have separate pages. Also, it would be a good idea to make the bulk of this page deal with general strategies for proving trigonometric identities. I am not confident that whoever wrote most of this page understands those techniques. He or she also does not understand how to avoid the hideously ugly formatting now on this page. I've edited many thousands of Wikiepedia math articles; I know what I'm talking about. Michael Hardy 19:09, 13 December 2006 (UTC)

I agree with Michael that it is reasonable to keep the pages separate. Gaussmarkov 16:54, 23 January 2007 (UTC)

[edit] Organization

Let's give names to the sub-types of identities, and to each identity, so the readers can find the ones they are looking for. Examples: Pythagorean, inequality, angle sum, etc. "Identity # 62" does not help much. Also, since the reason for this article is proofs, having the identity as a main point and the proof as a sub-point does not make sense to me. --MathMan64 20:27, 20 October 2006 (UTC)

Well I only gave 1 proof for each identity, but in case of more than one proof, it can be listed as a sub-point of the identity. --Ķĩřβȳ♥ŤįɱéØ 00:48, 21 October 2006 (UTC)
Let's label the headings for multiple proofs with descriptions such as:
=== Cotangent ratio ===
==== from definition ====
{ as is in article }
==== from reciprocal ====
{ new proof plan }
--MathMan64 01:50, 21 October 2006 (UTC)
That's fine with me. But the only problem I forsee is, some of these identities just don't have names. Sure, we have some easy ones like "Law of Sines" or "Law of Cosines", but what would we call something like \lim_{\phi \to 0}\frac{\sin k\phi}{p\phi} = \frac{k}{p} ? I've never seen that named in a textbook, it's just given without a name. --Ķĩřβȳ♥ŤįɱéØ 02:18, 21 October 2006 (UTC)

[edit] tangent inequality

The tangent inequality is not true for all angles. The tangent of π is zero. So tan π over π is not greater than one. --MathMan64 18:24, 29 October 2006 (UTC)

Oh, I forgot to restrict the domain. I'll fix it. --Ķĩřβȳ♥ŤįɱéØ 01:48, 30 October 2006 (UTC)

[edit] identities involving calculus

The previous proof of the Sine and angle ratio identity is circular as noted in A Circular Argument, by Fred Richman, The College Mathematics Journal © 1993. The result follows immediately from the definition of the length of an arc. So I changed the proof to reflect this. I left out a step, pending any discussion: the longest polygonal path for a given number of points on the arc is the one with equal length chords.

Gaussmarkov 23:45, 10 November 2006 (UTC)

I understand the logic behind this step and I too think that the previous proof was inadequate. However, I think the current proof needs to be elaborated because it doesn't go into details, and to the average reader, it doesn't mean much. CommandoGuard 15:51, 12 December 2006 (UTC)
Hmmmm...I just read "A Circular Argument" and the impression I was given by it is that any geometry-based proof of the limit in question which is correct and not circular is always more of a definition than a proof, no? CommandoGuard 13:52, 13 December 2006 (UTC)
Yes, some sort of limit argument is needed. In my opinion, the arc length needed for the current version should be made explicit and referenced to another location in the Wikipedia. That is what I did previously. In the present form, the angle and the arc length are implicitly equated and there is no justification for this. Gaussmarkov 16:51, 23 January 2007 (UTC)

[edit] messy, messy, messy

This is a really messy article in two ways (at least):

  • Formatting, typesetting, etc. See my most recent edit.
  • Logical structure. One may prove the identity A = E by writing A = B = C = D = E. That's what I did in my most recent edit. One may also prove A = E by saying A = E if blah, and blah is true if blahblah, and blahblahblah is true if etc.etc., and etc.etc. is a known truth (but one must be sure not to write "If A = E then ...."; the "if...then..." has to go in the right direction.

Michael Hardy 01:55, 17 November 2006 (UTC)

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