Talk:Trigonometry

Overlap

There seems to be a substantial overlap between Trigonometry (as the study of trigonometric functions) and Trigonometric functions, the former of which I just translated, which made me wonder what should go where. Does the "common trigonometric values" table belong here? Mnemonics? Does the "inverse trigonometric functions" section belong to Trigonometric functions? Should more be said about Fourier analysis here? Differential equations related to trig. functions? I understand no one is quite happy with this article (@Jacobolus!), and also that no one has time for a good rewrite, so how about we do some pruning here and there, so there's at least a little less overlap? There's this m:List of articles every Wikipedia should have/Expanded/Mathematics that lists both articles as (somewhat) vital, but no wiki, from what I can tell, has a clear separation between the two. Thoughts? Ponor (talk) 16:13, 27 June 2024 (UTC)

Substantial overlap is not a problem, as long as two articles don't have the same scope. This article trigonometry should be a much expanded high-level overview rather than a reference work, and should definitely discuss more about Fourier analysis, differential equations, etc. Overall what this topic needs is better sources and significant expansion, especially of prose, not pruning.

We should aim for complete and reasonably self contained separate articles for, among others, angle (currently a mess), angle measure (redirects), unit circle (incomplete and mediocre), history of trigonometry (incomplete and mediocre), trigonometric table (incomplete and mediocre), trigonometric functions (far too formula heavy), trigonometric scale (or similar title; we currently have the start of an article scale of chords, so it could be moved and expanded), logarithmic trigonometric functions (no current coverage of the topic), chord (trigonometry) (redirects), sine, tangent (trigonometry) (redirects), secant (trigonometry) (redirects), versine (needs a rewrite), half-tangent (i.e. the tangent of half an angle, red link), exsecant (I recently cleaned this one up), inverse trigonometric functions (not accessible enough), possibly arcsine and arctangent (both redirect), solution of triangles (needs more sources and historical discussion), ...

And then we should have separate articles for all of the major theorems and identities. Law of cosines is passable but needs sources for proofs. Law of sines needs work. They generally get weaker from there. Pretty much every section at list of trigonometric identities, e.g. angle sum identity, should be backed by a separate article. The article Proofs of trigonometric identities should be deleted and any salvageable content merged into articles about each separate topic.

Our article about spherical trigonometry is a complete mess. We should have separate articles about spherical triangle (redirects), spherical excess (redirects), polar triangle (redirects), polar duality (red link), Girard's theorem (redirects), Napier's analogies (redirects), Delambre's analogies (redirects), ... –jacobolus (t) 17:29, 27 June 2024 (UTC)

Hyperbolic functions?

Trigonometry is the study of circular functions; is there an analogous name for the stufy of hyperbolic functions? I'd like to add a {{distinguish}} hatnote if a suitable article exists. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:18, 22 August 2024 (UTC)

No, but you could consider it to be part of trigonometry if you want, and add a section down near the bottom of this article. –jacobolus (t) 15:46, 22 August 2024 (UTC)

Spherical trigonometry

I'm considering adding {{about|triangles in the Euclidean plane|triangles on a sphere|Spherical trigonometry|the album|Trigonometry (album)|the TV series|Trigonometry (TV series)}}. Is that enough, or does the article need a new section with a {{main}} template? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:23, 2 September 2024 (UTC)

Per WP:RELATED, this isn't the intended use of hatnotes. Instead, the lead section of this article should mention Spherical trigonometry with a link, and it should ideally include a dedicated section with a {{main}} link. –jacobolus (t) 18:10, 2 September 2024 (UTC)

Semi-protected edit request on 14 December 2024

REMOVE the link from the word 'adjacent' in the definition of Cosine and instead CHANGE it to an italicisation of it so it connotes that the word is being turned into a standard trigonometric term. Ideally, you could add a paragraph *before* the trigonometric definitions where the words 'opposite' 'adjacent' and 'hypotenuse' are defined. For a person not versed in trig, the word 'adjacent' could be either of the two sides that make the angle and the current phrasing is not pedagogically explicit that a standardized term is being introduced. Regardless, the hyperlink needs to be removed because it takes you to a useless target. The current link takes you to an article that has NO mention of the word 'adjacent' as used in trigonometric ratios. Thanks. 24.161.66.164 (talk) 18:05, 14 December 2024 (UTC)

 Done I moved the paragraph with term definitions in front of the trig definitions and removed the redirected link to triangle from 'adjacent'. I did not take the step of changing bolded font to italics, and have no preference if another editor chooses to do so. DrOrinScrivello (talk) 20:57, 14 December 2024 (UTC)

Reference to Baudhayana's Sulba Sutra

I acknowledge the revert regarding the distinction between cord geometry and angular functions. Rather than claiming that Baudhāyana developed trigonometry, would editors object to a one-sentence historical bridge noting that later Indian trigonometric tables (such as Āryabhaṭa's half-chords) relied geometrically on the earlier Śulbasūtra diagonal and similarity rules, as noted by T. A. Sarasvati Amma (1979, p. 58)? @Myuoh kaka roi Bookaddictt (talk) 08:34, 17 September 2026 (UTC)

baudhyana sulbasutra isn't related to trigonometry but rather related to geometry as it lacks angle measurement nor ratios and aryabhatta half chord related to sulbasutra diagonal and similar rules need more reliable sources to back the statement as need additional references apart from T. A. Sarasvati Amma (1979, p. 58) as I known reliable sources like kim plofker Mathematics in India doesn't mentions anything related to sulbasutra influence on aryabhatta half chord as indian mathematics in classical era trigonometry was influenced from Greek hipparchus tables which they converted into half chord and also the history section should be the summarisation on historical development in trigonometry and shouldn't be extended further as it should be added on History of trigonometry. Myuoh kaka roi (talk) 08:48, 17 September 2026 (UTC)

I think you are referring to this quotation

The whole of Indian geometry and trigonometry is dominated by the theorem of the square on the diagonal. The study of rational figures which fills pages in later mathematical texts, the sine-table and even much of algebra is based on this theorem. The field of influence of the principle of proportionality is even wider, holding sway as it does, over the whole of Indian mathematics.

It has been already discussed in Talk:History of trigonometry#The Sulba Sutras so it says that much of later indian mathematics is influenced with the theorm which also includes algebra.So it isn't only applicable to later trigonometry development but also in later algebra development in India.Its better to add the influence of sulbasutra theorm of diagonal in History of trigonometry rather than the history section of this article as the history section is already crowded and its only need to focus on important development of trigonometry rather than rely on theorm which had influence on later Mathematical development of India. Myuoh kaka roi (talk) 09:27, 17 September 2026 (UTC)