Talk:Trigonometric functions

Article
i wanted to learn something - completely impossible from this article, this is just a reference for those who know all of this material already. — Preceding unsigned comment added by 108.84.184.142 (talk) 21:44, 10 March 2013 (UTC)


 * i agree, the definition is supposed to be comprehensible without too much reference or dependence on other "terms". it was obviously written by those who already understand the subject and can't intuit how to explain it for those who don't. 197.134.147.164 (talk) 11:03, 15 May 2013 (UTC)


 * I also agree. This article seems to cry out for a bold rewrite. Stigmatella aurantiaca (talk) 02:27, 2 July 2013 (UTC)


 * I also agree. It is so disappointing that there are no surface plots of the absolute value for the complex trig functions. This "Domain coloring" is lame and impossible to decipher (it is completely ridiculous that I have to ask maple or mathematica to gain a reasonable quantitative understanding) 69.131.208.241 (talk) 21:49, 24 November 2021 (UTC).
 * The domain coloring method is "lame"? Please explain. It is true, though, that the type of the coloring used in the article (introduced by the user Nschloe) is very non-standard. A1E6 (talk) 16:43, 25 November 2021 (UTC)

I would like to point out that an encyclopedia article is not supposed to be the first place to learn about something. First consult a textbook, then for things that a textbook might leave out, or might get wrong, or might be slanted about, then go consult the encyclopedia. Or, first consult the encyclopedia in order to get a very vague and general idea of what is involved in the topic, what it is about, and a list of textbooks or sources in its bibliography. So these comments are invalid. 98.109.232.157 (talk) 05:06, 1 September 2014 (UTC)
 * OK, almost eight years old, but this statement is too outrageously ridiculous to leave alone. OF COURSE, an encyclopedia is supposed to be the first place to learn about something.  That's exactly why people used to buy Encyclopedia Britannica, Encyclopedia Americana, Colliers, Funk & Wagnalls ...  A question would come up in the family--that's where they'd go to look; Mom and Dad would encourage the kids to look things up.  And yes, I think that if an encyclopedia is supposed to be general interest (which I think Wikipedia is) and not a specialist reference for specialists, it should make an effort to say what a thing is about in some way--at least as much as the topic will allow--that anybody can understand it.  On tech and math subjects, Wikipedia falls woefully short in that regard. Uporządnicki (talk) 14:42, 30 April 2021 (UTC)
 * Wikipedia is a "reference" (can a math reference even be labeled as "non-specialist"?), not a textbook (WP:NOTTEXTBOOK). Sometimes, the articles are too technical and are marked as such, but that rarely happens. This article is not one of them and the editors are doing their best to make the article understandable. But I don't think it's possible to write a math reference so that anybody can understand it. A1E6 (talk) 16:38, 25 November 2021 (UTC)

Boy I hope that is not the purpose of Wikipedia. That would make it pretty useless. 4 July 2017 (JCBoone) — Preceding unsigned comment added by Joseph C Boone (talk • contribs) 21:50, 4 July 2017 (UTC)

Algebraic value of sin 45°
reverted my change from


 * $$\sin \frac\pi4 = \sin 45^\circ = \frac{\sqrt{2}}{2} = \frac{\sqrt2}2$$

to


 * $$\sin \frac\pi4 = \sin 45^\circ = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt2}$$

with the comment "Sqrt(2)/2 is much more common than 1/sqrt(2) in the literature". Though I understand that &radic;2/2 is more common, the line gives it twice. I wonder if it may help learners to know that both expressions are valid, should they come across the rarer form. Does anyone have any thoughts on this?

Cheers, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 22:55, 5 July 2020 (UTC)
 * added the accidentally duplicate values on 23 January 2020. Previously, the values looked like this and the duplication probably came from the "easy way to remember" values. Probably best to omit. Johnuniq (talk) 23:57, 5 July 2020 (UTC)
 * Yes, I already removed the duplicate values: . - DVdm (talk) 06:33, 6 July 2020 (UTC)
 * It might make sense to add a note to show it either way Bera678 (talk) 12:42, 17 December 2023 (UTC)

Asymptote oversight?
I'm surprised that there's no mention at all of how the tangent function has a vertical asymptote at $θ = (k + 1⁄2)\pi$, as it's what clearly delineates tan from sin and cos. Tangent (function) redirects here so I think it deserves mentioning, but I'm not sure on the best place for it as this article is quite dense already. Snizzbut (talk) 16:16, 28 February 2021 (UTC)
 * Good point. Also, the basic properties as functions of trigonometric functions were also lacking. I have added them, with a figure, at the beginning of section "In calculus". D.Lazard (talk) 17:24, 28 February 2021 (UTC)

Values of zero in table?
In the "Simple algebraic values," is there some reason not to show zeroes for the sine and tangent of 0°, and for the cosine and cotangent of 90°? Right now, those spaces are blank. That seems odd, considering that other spaces on the table show infinity; that's an arguable point--the zeroes are not. Uporządnicki (talk) 13:52, 19 August 2021 (UTC)
 * ✅. I replaced the tagged zeros with templates as in the first column. See . - DVdm (talk) 14:05, 19 August 2021 (UTC)
 * Test:
 * " $$0$$ " produces "$$0$$" (nothing), where " $0$ " produces "$0$".
 * " $$1$$ " produces "$$1$$".
 * " $$00$$ " produces "$$00$$".
 * " $$01$$ " produces "$$01$$".
 * " $$0=0$$ " produces "$$0=0$$".
 * " $$ 0$$ " produces "$$ 0$$". HA, we need a space!
 * Strange - DVdm (talk) 14:10, 19 August 2021 (UTC)
 * For consistency, I went back to " $$ 0$$ " with the spaces: . - DVdm (talk) 14:33, 19 August 2021 (UTC)
 * Silly me! I was just going to go in and type "0"! Uporządnicki (talk) 16:37, 19 August 2021 (UTC)
 * Not silly, as it seems to produce the same as " $0$ ". I tried that but that would give inconsistent results when rendering math as PNG. I've asked at Village pump (technical). Let's see what they say... - DVdm (talk) 17:07, 19 August 2021 (UTC)

Update. Known bug, introduced today: T288846,  - DVdm (talk) 21:28, 19 August 2021 (UTC)


 * Well, I meant "silly me" ironically--tongue-in-cheek suggesting that it was silly to think of trying the obvious: I want to show 0, type 0. I'll have to take your word for it that it will raise some sort of problem in Papua-New Guinea. Uporządnicki (talk) 11:54, 20 August 2021 (UTC)

Unit Circle Diagram
Contains a number of errors. I'm not in a good position (ie. edit SVGs) to correct them. The value for sixty degrees is given as
 * $$\sin \frac\pi3 = \sin 60^\circ = \frac{\sqrt{3}}{2} = \frac{1}{2}$$

which is not the case. It's correct in the table next to the diagram. Mwasheim (talk) 14:55, 9 April 2023 (UTC)


 * Sorry, in my understanding it says:
 * $$(\cos,\sin)(\frac{\pi}3) = (\cos,\sin)(60^\circ) = (\frac{1}{2},\frac{\sqrt{3}}{2})$$,
 * which is correct. –Nomen4Omen (talk) 15:08, 9 April 2023 (UTC)


 * Um, that is correct. Hmm. I was busy converting between radians and degrees and didn't read the legend carefully enough. Thanks! Mwasheim (talk) 15:21, 9 April 2023 (UTC)


 * as an aside, I wonder if it would help people sitting there with calculators which use radians (ie. all?) to specify that sin 90 is generally sin(rad(90)) on calculators?

SOHCAHTOA
@D.Lazard et al., I have heard many people talk about "SOHCAHTOA". Although I don't have a citation at hand, I think it is improvement to the article to discuss SOHCAHTOA. Hopefully, someone will come up with a citation pronto and this will all be moot but, even if not, might we keep this discussion anyway? — Q uantling (talk &#124; contribs) 13:14, 29 September 2023 (UTC)


 * This is discussed at Mnemonics in trigonometry. You can navigate to SOHCAHTOA to see the relevant section. –jacobolus (t) 13:48, 29 September 2023 (UTC)

Merging pages
I was on this page and I became curious: why do tangent, cotangent, secant and cosecant all share a page while sine and cosine get their own? Why can't we move them all into one page? Snipe (talk) 01:16, 23 November 2023 (UTC)


 * These were merged (a long time ago) because it was thought that most relevant material about any of them would be applicable to all of the others, many relevant features would be useful to compare from one to another, and important context was needed in common between them. People thought separate articles would consist of substantially duplicated material.
 * In retrospect I think this was the wrong decision (or rather, I think we should have an article called trigonometric functions about some common features and also have separate articles). Having these lumped together has discouraged people from adding useful information which applies to only one or another. Any subject which has enough to say about it independently to flesh out a self-contained article should generally have one, and there is quite a lot to separately say about sine, tangent, secant, etc., especially discussion about history. I eventually intend to make separate tangent (trigonometry) and secant (trigonometry) pages, and would be opposed to getting rid of the sine and cosine page, which should in my opinion also be expanded and somewhat reorganized. –jacobolus (t) 05:37, 23 November 2023 (UTC)

Notes and References
In the article, there are references in the notes section and another section of references in the references section. This error (if it is an error) makes it impossible to annotate the article. Please someone fix this bug Bera678 (talk) 14:01, 17 December 2023 (UTC)


 * There are a variety of reference styles used in Wikipedia articles, and this is one of the more common ones. If you add a source which will be used repeatedly, especially a long source with separate page numbers for the different claims, put it into 'references' and then cite it with a shortened citation in the footnotes. If you add a source used for just one claim, or a source used a few times but which is short enough to not need a page specified or where the pages used are the same for all cited claims, put it directly into a footnote. Feel free to also add textual notes to the 'notes' section. –jacobolus (t) 16:09, 17 December 2023 (UTC)
 * But this prevents adding notes to the article? Bera678 (talk) 16:48, 17 December 2023 (UTC)
 * I don't understand what you mean. What kind of note are you trying to add? Feel free to mix textual notes in with the reference footnotes. If you get consensus here, e.g. if you plan to do a substantial rewrite of the article, you can probably do some amount of reformatting of the appendices. –jacobolus (t) 16:51, 17 December 2023 (UTC)
 * To add notes to the article, the command must be used in the notes section. Bera678 (talk) 08:47, 19 December 2023 (UTC)
 * Feel free to add textual notes to the numbered footnotes currently in the article. You can add these with . –jacobolus (t) 09:11, 19 December 2023 (UTC)

"Logarithmic sine" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Logarithmic_sine&redirect=no Logarithmic sine] has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached. 1234qwer1234qwer4 23:22, 29 January 2024 (UTC)

tg should not be used.
tg and ctg, arctg and arcctg should not be used in accordance with ISO IEC 80000-2:2009. That is absent at the article. Voproshatel (talk) 19:01, 4 February 2024 (UTC)


 * yeah i also kind of agree User:Hamterous1 (discuss anything!🐹✈️) 00:25, 17 April 2024 (UTC)
 * Different countries and different authors had/have different conventions about this. In modern English language sources "tan" is the most common, partly because it is the only one supported by default in LaTeX. But if you look at work from France, Germany, or Russia, especially historical sources, you will commonly find "tang" and "tg" as an alternative. The current text in the article is fine, but if someone can find a clear discussion of this it would also be fine to more explicitly describe the relative popularity and extent of these various symbols. –jacobolus (t) 01:43, 17 April 2024 (UTC)
 * Oh, ok User:Hamterous1 (discuss anything!🐹✈️) 11:50, 17 April 2024 (UTC)