Talk:Spherical law of cosines

message: An anonymous contributor just added, without sources:
:The law of cosines could be also used to solve for angles, in this case it states:
::\cos(A) = -\cos(B)\cos(C) + \sin(B)\sin(C)\cos(a) \,
I haven't seen this before, and since no sources were provided and I don't have time to check it right now, I've removed it from the article.  Feel free to provide a reputable source and add it back.  Or maybe there is some trivial argument to derive it from the ordinary form of the law of cosines that I'm missing right now?
—Steven G. Johnson 15:48, 3 July 2006 (UTC)
replies: text: We still need a reference for this.  —Steven G. Johnson (talk) 04:44, 26 August 2008 (UTC)
replies: text: The formula is entirely legit; it's probably in Bowditch (I'll confirm that) and it's certainly in other collections of spherical-trig formulas. Tim Zukas (talk) 16:49, 24 August 2010 (UTC)
replies: text: I already added a reference for this formula some time ago. — Steven G. Johnson (talk) 09:25, 25 August 2010 (UTC)
thread_title: Variant for angles?

message: "The sea is sissy and crass."
  1)    c  =  c  c   +  c s s
  2)   cos = cos cos + cos sin sin
  3)     a       b     c       A     b     c
  4) cos a = cos b cos c + cos A sin b sin c
Q.E.D.
For angles, just change the sign and cases:
  cos A = cos B cos C - cos a sin B sin C
(Invented by me, Marshall Price of Miami, while sailing to Newport, RI, circa 1983. All rights abandoned.)
D021317c 23:42, 23 March 2007 (UTC)
thread_title:  Mnemonic 

message: Some of the links on the page referred to in "Romuald Ireneus 'Scibor-Marchocki, Spherical trigonometry, Elementary-Geometry Trigonometry web page (1997)" are broken, but by changing the extensions of the URLs from ".htm" to ".html", most of them work.D021317c 00:31, 24 March 2007 (UTC)
thread_title: Broken links

message: Is there any one person (or group) that originated the spherical law of cosines?  —Preceding unsigned comment added by 146.227.1.12 (talk) 12:45, 22 August 2009 (UTC)
thread_title:  Origins of formula 

message: The first paragraph defines lowercase letters as sides, uppercase letters as angles.  Then we present a formula that takes the sine/cosine of both types of variables, only later adding that for the special case of the unit sphere, the lengths of the sides are numerically identical (in radians) to the central angles subtended by those sides.
Given that this is a narrowly focused article written specifically to explain a single formula, this seems sloppy and unnecessarily confusing.  I would encourage someone who knows the subject matter to create a better graphic showing and labeling the central angles separately from the sides of the spherical triangle, and listing formulas that use only angles as arguments to trig functions.
Ma-Ma-Max Headroom (talk) 03:06, 11 March 2011 (UTC)
replies: text: I couldn't agree with you more, the notation in this article was driving me nuts with it using lengths as angles in the arguments to functions which require angles. The article is simply wrong in this regard and requires some a/R, b/R, c/R substitutions for a, b, and c, when used in the trig function arguments. MrInteractive (talk) 00:14, 16 August 2022 (UTC)
thread_title:  Consistency 

message: We have four proofs in the article.  I propose that we remove the first two.  I don't find them to be particularly elegant or intuitive.  What do you think?  64.132.59.226 (talk) 15:21, 13 February 2018 (UTC)
replies: text: I am going ahead and making this edit.  If you disagree, please consider this an instance of the BOLD, revert, discuss cycle; please undo the edit to the extent necessary and comment here as to what you would like to see and why.  64.132.59.226 (talk) 15:11, 20 February 2018 (UTC)
thread_title:  Eliminating some proofs