Trigonometry was a Mathematics good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article milestones Date Process Result February 23, 2009 Good article nominee Not listed

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How to proof identies Please help me @Pi 2 41.121.19.115 (talk) 13:44, 25 April 2024 (UTC)[reply]

This is a place for discussing how to improve this article about trigonometry, not a general help forum about trigonometry. I would recommend you try someplace like http://reddit.com/r/learnmath instead. –jacobolus (t) 14:42, 25 April 2024 (UTC)[reply]

A user insists to add in the first paragraph of the lead a sentence about "polygonometry". I'll to revert them again for the following reasons.

• "Polygonometry" is not a commonly used word nor a known area of mathematics
• the link to generalized trigonometry is wrong (this article is about trigonometry in non-Euclidean spaces)
• The assertion that every polygon can be decomposed into triangles is true but has nothing to do here
• The formulation suggests wrongly that polygonometry is more important than trigonometry
• Computation of angles and side lengths of polygons is certainly an application of trigonometry, but it is not its heart.
• Over all: the first sentence is for a short description of the subject, not for its possible uses.

This said, I would not oppose to add to the third paragraph of the lead (the one about applications), a sentence saying that trigonometry can be used to compute angles and side lengths of every polygon. D.Lazard (talk) 15:02, 26 May 2024 (UTC)[reply]

@D.Lazard: some good points above, thank you. My priority here is to establish the core notability of trigonometry. Per WP:LEAD, a good lead section cultivates interest in reading on… in a clear, accessible style… [and should] establish context, [and] explain why the topic is notable.

At the moment the lead is missing the most important point - that trigonometry is not really just about triangles. It is the foundation for the study of all polygons.

Having said this, I would prefer to widen the point further, to explain why trigonometry is foundational to so many branches of mathematics. It all comes down to the point that triangles are the simplest polygon.

Onceinawhile (talk) 15:44, 26 May 2024 (UTC)[reply]

Please, do not present your opinion as facts: Trigonometry is not foundational for any branch of mathematics. It is a part of geometry that is used as a computational tool in many applications of geometry. Historically, the application of trigonometry that can be called fundamental (not foundational) is spherical geometry, and its applications to navigation and celestial mechanics. This is historically, as wells as nowadays, much more important than the applictions to geometry of polygons; this is the needs of these applications that motivated the invention of trigonometry. Another fundamental application of trigonometric functions is Fourier analysis. Clearly, polygons are not involved an any of these applications.

Again, do not present your opinion as facts, and the importance that you give to the study of polygons is only an opinion. D.Lazard (talk) 17:27, 26 May 2024 (UTC)[reply]

Your comment orders me twice to "not present [my] opinion as facts", whilst the main body of your comment is presenting your opinion as facts.

If your position is more correct than mine, you need to bring sources for it. So far you have provided no sources, whilst deleting three of my sources and quotes.

Onceinawhile (talk) 21:43, 26 May 2024 (UTC)[reply]

There is no problem to present in talk pages personal opinions on how present things in articles. I know that what I wrote is my opinion, and this is the reason for which I never try to add them on the aricle. But the existence of argumented opinions that challenge what you wrote in the article is strong indication that you tried to present your opinion as fact in the encyclopedia. D.Lazard (talk) 08:58, 27 May 2024 (UTC)[reply]

The name "trigonometry" is bit of a misnomer, as the subject of trigonometry is not primarily about measuring triangles (some people prefer the name "goniometry" which is more accurate), somewhat similar to the way "geometry" is not primarily about measuring the earth. Trigonometry's primary focus is relating circular arc lengths / angle measures to straight line segments (and using similarity, to abstracted line segments / coordinates based on a standard circle for which a trigonometric table or "trigonometric function" is defined, which can be dilated to fit any desired circle). As D.Lazard points out, the original application was to spherical geometry in the form of spherical trigonometry, for use in astronomy, but later also celestial navigation, geodesy/cartography, and much later also geology, crystallography, etc. Planar trigonometry was eventually used for optics, surveying, gunnery, architecture, trades, engineering, ..., but again while there were often triangles involved, the most fundamental feature was usually circles.

Solution of (right or general) triangles is one particular application of trigonometry which arose in medieval Islamic mathematics and then was further developed in Renaissance Europe. It's an important application which is especially central to teaching in high school courses, but is still not really the foundation of the subject.

In the past century or two, trigonometry is more generally the study of trigonometric functions, for which more advanced applications involve quite a bit of mathematical analysis. The "circles" which show up are a bit abstract, describing for instance the domain of arbitrary periodic functions, which makes trigonometry important to the study of differential equations, signal processing, etc.

"Polygonometry", meaning the study of metrical relations of polygons including angle measures, is a relatively niche topic dating from the 18th century and rarely presented systematically. Polygons are instead studied from a variety of points of view in various applications. The application which is closest to what might be called "polygonometry" is probably the kinematics of linkages. You could also consider surveying to involve a lot of "polygonometry" but it's not really thought of that way as far as I can tell. In computational geometry there is significant study of polygons, but usually based on analytic geometry and vectors rather than angle measures. –jacobolus (t) 07:55, 27 May 2024 (UTC)[reply]

Thank you jacobolus. This is a helpful build - per above we need to make clear in the lead that "trigonometry is not really just about triangles". I will try to bring a few more sources from differentt perspectives. Onceinawhile (talk) 08:16, 27 May 2024 (UTC)[reply]

@D.Lazard and Jacobolus: I have taken the time to read this talk page more broadly, particularly the core definition. I see that in January there was a debate about this edit which then petered out. This is the same problem that triggered me to edit here in the first place. It is simply misleading to suggest that trigonometry is just about triangles. The Glen Van Brummelen quote that jacobolus provided sets it out nicely (see here for convenience, and the "What's in a name?" section in volume 2). Since Van Brummelen's two volumes in the Princeton University Press represent the most detailed broad-concept study of the topic that has been published, our article should follow his explanation.

As an aside, for an illustration of how much our readers would benefit from a clear and well-sourced dispelling of the myth that trigonometry is just about triangles, look how frequently this same issue comes up elsewhere on the internet ([1][2][3][4]).

Onceinawhile (talk) 16:32, 1 June 2024 (UTC)[reply]

Yeah, I would like to eventually do a substantial rewrite of this page. It's just a bit of a daunting project that takes finding some substantial time and a bit of pep talk to get motivated to take on. It's a lot easier to respond to occasional talk page discussions. :-) –jacobolus (t) 16:54, 1 June 2024 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

 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)[reply]