Talk:Law of sines

Rework the ambiguous case

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,

1. the section on "the ambiguous case" refers to a completely different problem of determining a triangle from 2 sides an 1 angle and
2. 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)

Variables

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)

inscribed angle instead of central angle in the "proof" of "Relation to the circumcircle"

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)

A Typo Should be Corrected.

I tried to determine where Brahmagupta's version of the Law of Sines comes from and followed the reference in this article. However, I found the reference "Wilson, H.J.J., Eastern Science, John Murray Publishers, 1952, p46" is incorrect. As a result, the reference page "Law of sines#cite ref-2" is also incorrect. The author should be H. J. J. Winter rather than H. J. J. Wilson. This is the book on Amazon: https://www.amazon.com/dp/B0000CI5YE/ref=pe_386300_440135490_TE_simp_item_image, which shows clearly that the author is H. J. J. Winter rather than H. J. J. Wilson.

Could someone modify the original page?

Thanks. Ching-Kuang Shene (talk) 09:23, 4 April 2024 (UTC)

The history section here is incomplete and kind of a mess. If I get some time and feel motivated at some point, I might try to find some better sources and somewhat rewrite it. Feel free to give it a shot though.

As for this specific point, the author is HJJ Winter. Here's a scan, https://archive.org/details/easternscienceou0000wint/page/46/ (you need to make a free Internet Archive account and "check out" the book to view this page). –jacobolus (t) 19:02, 4 April 2024 (UTC)

@XOR'easter thanks for the moderate cleanup here. We should probably not directly attribute these uncontroversial claims to specific scholars at all, but just make direct statements giving sources in the footnotes. –jacobolus (t) 22:25, 19 June 2024 (UTC)

Though while we're at it, we might want to be a bit cagier about crediting Brahmagupta; the example involved is an equation that is algebraically related to the law of sines, used for calculating the distance from the Earth to another planet in a planetary theory involving epicycles, but is not quite the same relation, and is not treated as a general tool for solving triangles. Here's what Van Brummelen says: "Whether or not this apparent use of the Law of Sines allows us to claim independent knowledge of it for Brahmagupta is a delicate matter..." It might be best to directly describe what Brahmagupta did, including a diagram, instead of speculating about what he might have thought about it. –jacobolus (t) 23:24, 19 June 2024 (UTC)

What winter is saying is that Brahmagupta stated a rule which we now express in the form 2r=a/sin a = b/sin b = c/sin c. He never said that he stated the given formula. Hu741f4 (talk) 04:56, 30 October 2024 (UTC)

Yes, but that's also not really true, or at least is substantially misleading without a lot of careful qualification and explanation. –jacobolus (t) 05:21, 30 October 2024 (UTC)