Talk:Law of cosines

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WikiProject Echo has identified Law of cosines as a foreign language featured article. You may be able to improve this article with information from the French language Wikipedia.

Contents 1 Phythagorean Theorem also Proved by Law of Cosines? 2 Circular proof? 3 Section moving 4 Another use for Law of Cosines 5 We? 6 Rewrite

[edit] Phythagorean Theorem also Proved by Law of Cosines?

Okay, in the article, it states the since cos 90 is 0 the Law of Cosines is reduced to the Phythagorean Theorem. I don't think that's the case cause if a² = b² + c² − 2bccosA, then wouldn't a² = b² + c²? —The preceding unsigned comment was added by 70.107.165.59 (talk • contribs).

Yes, and that's the Pythagorean theorem (in the case where the right angles is the angle between the sides of lengths b and c). Michael Hardy 23:20, 1 March 2007 (UTC)

[edit] Circular proof?

In the dot product article, a dot b = a b cos theta is proved using the Law of Cosines. And the Law of Cosines is proved using vector dot products. Shouldn't somebody fix this? --Orborde 07:48, 9 September 2005 (UTC)

The dot product proof should be removed. It's circular. Law of cosines comes first historically and all of vector calculus is assumed to depend on it, not vice versa. Might as well use vectors to prove the pythagorean theorem. Pfalstad 10:22, 9 September 2005 (UTC)

I have hopefully solved this problem, by stating the law of cosines is equivalent to the dot product formula from theory of vectors. --345Kai 10:45, 30 March 2006 (UTC)

Wow that's pretty darn smart. --M1ss1ontomars2k4 | T | C | @ 04:04, 21 May 2006 (UTC)

[edit] Section moving

I removed the following section because this is said in the first paragraph and follows from elementary algebra:

[edit] Another use for Law of Cosines

The Law of Cosines can also be used to find the measure of the three angles in a triangle if you know the length of the three sides. This is how you do it: &nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp&nbsp

a² + b² − 2abcosC = c²

− 2abcosC = − a² − b² + c²

cosC = ( − a² − b² + c²) / ( − 2ab)

cosC = (a² + b² − c²) / (2ab)

C = arccos[(a² + b² − c²) / (2ab)]

Now you can find the measure of angle C!

— Sverdrup (talk) 21:00, 25 Feb 2004 (UTC)

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If noone objects, I'm going to put the vector-based proof first and move the other one down since the former is more simple and universal as opposed to the latter.. or someone else could do it.. or whatever... - Evil saltine 00:33, 22 May 2005 (UTC)

As noted above, the vector-based proof is circular: the proof that the dot product of two vectors has a geometric interpretation in Euclidian space is itself based on the law of cosines. So using the geometric interpretation of a dot product to prove the law of cosines is a bit problematic... --Delirium 03:17, 13 November 2005 (UTC)

see above --345Kai 10:45, 30 March 2006 (UTC)

[edit] We?

Is the usage of "we" throughout this article proper? Shouldn't "we can easily prove" be "can be proved" (wlong with some sentence rearrangement). BrokenSegue 04:00, 30 March 2006 (UTC)

[edit] Rewrite

I have rewritten the article and expanded it considerably. I have taken a lot of material from the French article, according to the above suggestion. I hope you like it!!! Please improve further... (and sorry that in the history of this page the big change was signed "Euklid". That was me and and I know we shouldn't use these kinds of names on Wikipedia, so I've changed my login. --345Kai 10:45, 30 March 2006 (UTC)