Talk:Law of sines

message: Could somebody please explain about the cyclic permutation part and how it is applied?
It isin't very clear...
Anyway, there is also another proof for the 2R, and it's much easier to understand. I found it on google.
Link: http://planetmath.org/encyclopedia/SinesLawProof.html
----  —Preceding unsigned comment added by 218.186.12.11 (talk) 18:01, 15 August 2008 (UTC)
thread_title:  Cyclic permutation part 

message: One of the main reasons that I use wikipedia for information on formulas over math world is because I do not normally get bombarded by theory and the inner workings of these formulas but more how to use them and what they can do for me. I think that it would be much better if some examples were given, like how to use it for working out a side or an angle if you have the other bits of information.  —Preceding unsigned comment added by 84.92.106.157 (talk) 
:I agree.  The Triangle solution(s) and Triangle equality(-ies) pages need to be made. 75.35.201.48 11:32, 15 March 2007 (UTC)
thread_title:  Needs Some Work 

message: I made radians a link, so they can easily view what a radian is if they don't know already. That is trivial to solve these problems. Also, I will try adding some examples.
--chocolateluvr88 11:08, 5 January 2006 (UTC)
replies: text: but the law of sines is true regardless of the units used, no? Matt 12:51, 31 January 2006 (UTC)
replies: text: oh, except for the 2R part, which I didn't see before, never mind. Matt 12:53, 31 January 2006 (UTC)
replies: text: No proof is given for the =2R part, and the example at the bottom uses degrees for the example. Although I don't doubt that the =2R part is true, are you sure that it's part of the law of sines? my calculus text doesn't mention it. Matt 13:00, 31 January 2006 (UTC)
replies: text:  Proof is now given for the =2R part. Suck on that. (my friend did it) 195.168.237.121 17:26, 28 May 2006 (UTC)
thread_title: [[User:chocolateluvr88|chocolateluvr88]]

message: Why not change 2R to just D? Seems like it would be more in character for wikipedia. If the 2R term is convenient for the proof of the law of sines, or some other reason then it doesn't really matter. Please let me know though. Thanks
Guardian of Light 16:02, 31 May 2006 (UTC)
replies: text:  Please see proof. D would probably make it more unclear. I have never seen it replaced with D. The reason is probably the fakt that D is not as important in triangles as the radius of the inscribed triangle.. 195.168.243.36 12:27, 6 June 2006 (UTC)
thread_title:  Radius vs Diameter 

message: I am a 6th grader and for some strange reason need to know this... *psst* I think my teachers are dillsuional *cough* so I would really love it if you could put this formula in a more 6th grader like way... Thanks!  —Preceding unsigned comment added by 74.128.184.134 (talk) 01:31, 29 January 2008 (UTC)
thread_title:  Erm... 

message: It would be nice to have a history section, identifying when the law was first stated.
Is it in Euclid?  Jheald (talk) 10:30, 14 September 2008 (UTC)
thread_title:  History ? 

message: This is the final step in this article's proof section. Can anybody link me to an explanation of this step or help me out? Maybe the step needs to be a little more explicit. Thanks 98.199.206.122 (talk) 02:22, 20 September 2008 (UTC)
replies: text: I've commented out the whole section.  It said one should make an "axis" through b.  I couldn't figure out what that meant.  The illustration should a line through the vertex B but there was no indication of how one could know WHICH line.  Later it is implied that the line goes through the center of the circumscribed circle, but somehow one was to find that center by using that line, so it's as if one doesn't know where the center is at the time when one draws that line.  So how does one know where to draw that line?  No clue.  One could have drawn perpendicular bisectors of TWO sides rather than one, and they would have intersected at the center of the circumscribed circle, and then maybe the rest of the argument works.  But that's not what it said and not what the illustration showed. Michael Hardy (talk) 15:23, 20 September 2008 (UTC)

text: OK, I've found the edit where the proof was added and at that time it made sense, but was expressed in imperfect English.  I'll see if I can restore it to what it should have been. Michael Hardy (talk) 15:30, 20 September 2008 (UTC)
thread_title:  Applying cyclic permutation: 

message: The article cites Jacques Sesiano, "Islamic mathematics", p. 157, in  for the proposition The spherical law of sines was discovered in the 10th century by the Persian mathematician, Abu Nasr Mansur.  Unfortunately that book does not mention Abu Nasr Mansur at all.  On page 157 it does say: ... theorem 111.1) and gave rise through Abū׳l-Wafā׳ al-Būzjānī (940—997/8) to the law of sines for spherical triangles.  I am afraid that we must delete the reference as inapplicable.  Does anyone have a replacement citation to a reliable source that actually verifies Abu Nasr Mansur as the discoverer? --Bejnar (talk) 16:58, 15 April 2010 (UTC)
thread_title: Mansur citation problem

message: The term "hinge" is common among Riemannian geometers in the context of Toponogov's theorem (some call it Alexandrov's theorem).  Generalisations of the law of cosines to spaces other than R^n should be discussed there.  Tkuvho (talk) 11:18, 30 May 2010 (UTC)
thread_title:  wrong page 

message: Someone wrote a proposed proof that the usual identity for the sine of a sum follows from the law of sines:
: 
:: To prove this, make an arbitrary triangle with sides a, b, and c with corresponding arbitrary angles A, B and C.  Draw a perpendicular to c from angle C. This will split the angle into two different angles, α and β, that are less than 90 degrees.  Let α be on the left and β be on the right.
: 
The part about left and right makes no sense, since nothing before that had been specified as being on the left or on the right.  To people's diagrams could be mirror images of each other until they get to this line about α being on the left, and then they both put α on the left, and then one has angle α adjacent to side a and the other has α adjacent to b.
: 
:: Apply the sine law to side c and side a.
: 
This is unclear at best.  What does it mean?  Here's a guess: it means write the identity
: 
:  {\sin A \over a} = {\sin C \over c}. 
: 
Just a guess.
: 
:: Solve this equation for the sine of the multiple angles.
: 
Again unclear.  What are the "multiple angles"?  Does it mean solve for the sines (plural) if the two angles A and C?   That would give
:  \sin A = {a\sin C \over c}. 
and similarly for sin C, but we'd only be solving for each in terms of the other.
: 
:: Notice that the perpendicular makes two right angles triangles, also note that sin(A) = cos(α),
: 
But sin(A) = cos(α) only if α is on the same side that angle A is on.  If that is what was meant by "Let α be on the left, then it works only if A is on the left, although that was never stated.  Perhaps "Let α be on the left" really meant "Let α be on the same side that A is on."  We shouldn't be made to guess about these things.
: 
:: sin(B) = cos(β) and that c = a sin(β) + b sin(α).  After making these substitutions you should have sin(α + β) = sin(β)cos(α) + (b/a)sin(α)cos(α).  Now apply the sine law to sides b and a and make the substitutions noted before. Now substitute this expression for (b/a) into the original equation for sin(α + β) and you will have the angle sum identity for α and β in terms of sine.
: 
OK, from this I should be able to reconstruct it.  I think these things should have been written clearly in the first place. Michael Hardy (talk) 22:14, 13 August 2010 (UTC)
thread_title:  questions about a proof 

message: The section on the extension of tetrahedra claims to be about the Law of Sines, but there are only angles involved, no edge lenghths or triangle areas.  Other than that the presented formula has a bunch of sine functions in it, what makes it correspond to the ordinary two-dimensional case that relates sines to edge lengths?  I would remove this section of the article.  192.35.44.24 (talk) 21:08, 17 January 2013 (UTC)
thread_title:  Extention to tetrahedra? 

message: If you are given A, a, c in ∆ABC, then you can use the Sine Law to calculate at least one solution C_1 for C where C_1 = sin^-1 (c.sin A / a). If C_1 is not 90° degrees and a < c, then there exists another solution C_2 = 180° - C_1.
Danchristensen (talk) 19:55, 28 November 2014 (UTC)
thread_title:  Simpler Criterion for Ambiguous Case? 

message: Support: I don't see that the long proof, in three cases, adds any relevant information or intuition to why the Law of sines is true.  I move that we eliminate the long proof, retaining only the succinct proof based upon computing the area of a triangle with three different base edges.  Please indicate your opinion. 𝕃eegrc (talk) 11:59, 16 June 2016 (UTC)
thread_title:  Proposal to remove long proof, please vote 

message: The introduction mentions the triangle problem of determining a triangle from 1 side length and 2 angles, and refers to an ambiguous case.
This ambiguous case is later addressed right after the proof -- I understand this may be important for math homework (but it's really not relevant for this article).
However,
# the section on "the ambiguous case" refers to a completely different problem of determining a triangle from 2 sides an 1 angle and
# the same section is not self-contained in the sense that the problem statement is not even given in the first sentences while making unclear references to "the problem" and "the data provided". Provided where?
Rework or remove.
2A02:810D:14C0:1DF8:0:0:0:2 (talk) 04:01, 26 February 2017 (UTC)
thread_title:  Rework the ambiguous case 

message: This article uses different variables for the angles than law of cosines and law of tangents. That could be confusing to some. TVGarfield (talk) 19:14, 8 January 2018 (UTC)
thread_title: Variables

message: Should it be inscribed angles instead of central angles in the "proof" of "Relation to the circumcircle"?
Angles {\displaystyle \angle C}{\displaystyle \angle C} and {\displaystyle \angle D}{\displaystyle \angle D} are inscribed angles that intercept the same arc AB.  — Preceding unsigned comment added by 103.139.171.78 (talk) 14:30, 15 July 2020 (UTC)
thread_title:   inscribed angle instead of central angle in the "proof" of "Relation to the circumcircle"