# Talk:Trigonometric functions

Trigonometric functions is a former featured article. Please see the links under Article milestones below for its original nomination page (for older articles, check the nomination archive) and why it was removed.
This article appeared on Wikipedia's Main Page as Today's featured article on March 6, 2004.
Article milestones
DateProcessResult
December 12, 2003Featured article candidatePromoted
September 20, 2004Featured article reviewKept
July 19, 2008Featured article reviewDemoted
Current status: Former featured article
WikiProject Mathematics (Rated B-class, Top-priority)
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## 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 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)

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 (talkcontribs) 21:50, 4 July 2017 (UTC)

## Edits of December 2017

@D.Lazard::I implore you not to make any more edits to the main article for the rest of the day in your time region.@D.Lazard:: Please, just for the rest of your day. My edits and your edits have conflicted twice, which made me lost my work. And Why did you delete my proof of the fact that tanθ is the ordinate of B, cotθ is the abscissa of C, secθ is the abscissa of E, and cscθ is the ordinate of D? This morning and afternoon, my work of editing this article was interrupted twice by something that required me to leave the computer. That was why you could see some errors in my edits, because I couldn't finish my edit. Now I have time to finish it.Onmaditque (talk) 11:44, 30 December 2017 (UTC)

To Onmaditque: Please place new discussions in new sections at bottom of talk pages (automatically done by button "New section" at the top of talk pages).
In case of edit conflict, you should not lost your work: it suffices to follow the instructions of the edit-conflict page. Otherwise, you can go back to your last edit page, and copy the implied sentence(s) for pasting it (them) either in a new edit page, that may be your WP:sandbox page or the page that you were editing.
I have removed your proof for several reasons. Firstly it does not add anything useful to the article (see MOS:MATH#Proofs). Secondly, a succession of formulas without linking words is not a proof. Thirdly, you use vector notation, that should be too technical for most readers. By the way every proof should use geometric arguments, and the clearest proof depends on the geometric background of the reader. Thus any proof should be confusing for some readers, while no proof will add anything for understanding trigonometric functions (which are the subject). Thus it is better to not have a proof here.
About edit conflicts: Please provide edit summaries, and when you are planning further edits on the same part of the article, say it in the edit summary. D.Lazard (talk) 12:28, 30 December 2017 (UTC)

@D.Lazard:: Thank you for providing the reasons of removing my proof. I totally agree with these reasons,but I would like to ask why you reverted my two edits after DVdm? I think I fixed some inaccuracies in my edits. For example, I changed "the smallest period" in the sentence "The smallest period is π for the tangent and the cotangent and 2π for the four other trigonometric functions" to "the smallest positive period (called the primitive period)". Since the period of a periodic function can be negative, strictly speaking, a periodic function does not have the smallest period. It is also more accurate to say "That is, the identities

{\displaystyle {\begin{aligned}\tan \theta &=\tan(\theta +k\pi )\,,\\\cot \theta &=\cot(\theta +k\pi )\,,\end{aligned}}}

hold for any angle θ and any integer k." than to say "that is

{\displaystyle {\begin{aligned}\tan \theta &=\tan(\theta +k\pi )\,,\\\cot \theta &=\cot(\theta +k\pi )\,,\end{aligned}}}

for any integer k." What's more, I kept most of your words in my latest revision (the one before your reversion).I feel that you reverted my edits without even reading it. Neither did you provide a definite reason. What did you mean by "non-explained edits"? Remember "BRD is not a valid excuse for reverting good-faith efforts to improve a page simply because you don't like the changes" or even because you think your revision is the best.Onmaditque (talk) 06:53, 31 December 2017 (UTC)

You never provide any edit summary. This may be acceptable for minor edits that are easy to check. This is not for edits like yours, which require a careful check for knowing if they really improve the article, and for understanding their motivations. That is what I mean with "non-explained edits". This would be a sufficient reason for reverting your last edits. But there are several other reasons:
• A change of section heading requires a consensus a soon as some one disagree with it. This is the case here.
• Your edits are badly formatted and do not respect WP:MOS (using "&" instead of "and"; symbols for points sometimes in italic, sometimes not; displayed formula transformed into a non-breaking long formula; ...)
• The mention of "primitive period" is confusing here, as the term is used only in some branches of mathematics, and other terms are used elsewhere. Moreover, if you look where Primitive period redirects, you will see that it is not a good idea to suggest searching this phrase. Nevertheless, I could agree with your concern about "smallest", and I have added "positive" for clarification.
• About adding "for any angle" or changing "smallest period" into "smallest positive period": A mathematical text written for being understandable by a large audience cannot be formally correct. Therefore, a lack of accuracy is acceptable, and even recommended, if it is not mathematically wrong, if nobody would be confused by it, and if a better accuracy would make reading more difficult. It is why I have omitted "for any angle". For "smallest period", I am convinced that nobody would be confused, but I agree that it is mathematically incorrect, and deserves to be fixed, since this would not really complicate the sentence.
As you can see, it is not that I do not "like" your edits, it is that I disagree with them. Thus BRD applies fully. Nevertheless, I acknowledge that these are good faith edits. Otherwise, I would not have taken so much time for discussing them. D.Lazard (talk) 10:48, 31 December 2017 (UTC)

## Edits of January 2018

@D.Lazard:: Thank you for providing the reasons of reverting my edits. Your words made me know more about how to edit Wikipedia properly. There are some issues with your revision of the article that I would like to discuss with you.The term “identity” in the sentence “As a rotation of an angle of ±2π is the identity, point A is the same for two angles that differ from an integer multiple of 2π” is confusing, since the term is too technical for most readers to understand its meaning. Moreover, “two angles that differ from an integer multiple of 2π” means “two angles that do not equal an integer multiple of 2π”, so the original phrase “two angles that differ from an integer multiple of 2π” does not make much sense. In order to make the sentence easier to understand, I suggest that you rewrite it like this: “As a rotation of an angle of ±2π does not change the position or size of a shape, Point A is the same for two angles whose difference is an integer multiple of 2π”. --Onmaditque (talk) 01:02, 7 January 2018 (UTC)

Many thanks for your recent edits, which clearly improve my version. D.Lazard (talk) 15:13, 7 January 2018 (UTC)

## Removing of section "Computation"

I will remove section "Computation" for the following reasons. It is written in the form of an essay rather than in encyclopedic style. It WP:original synthesis mixing in an indiscriminate way some very elementary special cases, methods used before availability of computers, and methods used in old computers. The methods that are used presently by builtin functions in computers software are not even mentioned. Also IEEE 754 (which recommend the application of the norm to sine and cosine), and methods for very high precision are not mentioned. So the only true information that a non-specialist reader can extract from this section is that methods exist for the computation.

A section on methods for computing trigonometric functions could be useful if it describes the methods that are presently used in computers, but the present section is not a convenient starting point for that, and I guess that it would be too technical for this article. So WP:TNT seems the best way to proceed. D.Lazard (talk) 14:04, 26 April 2019 (UTC)

I support your initiative. Good information is available at Exact trigonometric constants so it should be linked, either in “See also” or elsewhere in the article. Dolphin (t) 06:10, 27 April 2019 (UTC)
Thanks! Dolphin (t) 08:41, 27 April 2019 (UTC)

## Basic identities

IMO, this section must contain only the basic identities that everyone who manipulates trigonometric functions must know and use. So for minimizing it, I see nothing else to remove than the formulas involving csc, sec, and ctg, which are not used in practice (using other trig. functions than sin, cos and tan makes every real-world computation much more difficult, because of too many choices). Also, the antiderivatives are useful in practice only for sin and cos, as, except for very simple expressions, the first thing to do for integrating is to convert everything into sin and cos.
On the other hand, the most important basic identities must be kept here, as it is here that a reader comes naturally for refreshing his memory of them. D.Lazard (talk) 17:12, 14 August 2019 (UTC)

## sinh and cosh

This article uses sinh and cosh without defining them or linking to a page with a definition. — Preceding unsigned comment added by Subcelestial (talkcontribs) 17:43, 15 November 2019 (UTC)

Fixed, with some text improvement. D.Lazard (talk) 18:02, 15 November 2019 (UTC)

## Who got rid of the Exsecant, Versine, and Excosecant?

These are also trigonometric functions.Eshaan11 (talk) 13:42, 5 May 2020 (UTC)

... and they are mentioned at the end of the history section, which is their right place, as explained there. D.Lazard (talk) 14:05, 5 May 2020 (UTC)

## My minor edits

@D.Lazard: What are the problems with my edits except a capitalization of "degrees"? Thanks Santosh L (talk) 04:22, 17 June 2020 (UTC)

Counterclockwise is typically one word. Although the hyphenated form is attested, there's no need to change it. Also, your changing of "expressed in" to "taken as" is awkward at best. –Deacon Vorbis (carbon • videos) 04:26, 17 June 2020 (UTC)

## Algebraic value of sin 45°

@DVdm: reverted my change from

${\displaystyle \sin {\frac {\pi }{4}}=\sin 45^{\circ }={\frac {\sqrt {2}}{2}}={\frac {\sqrt {2}}{2}}}$

to

${\displaystyle \sin {\frac {\pi }{4}}=\sin 45^{\circ }={\frac {\sqrt {2}}{2}}={\frac {1}{\sqrt {2}}}}$

with the comment "Sqrt(2)/2 is much more common than 1/sqrt(2) in the literature". Though I understand that √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,
cmɢʟeeτaʟκ 22:55, 5 July 2020 (UTC)

Crissov 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: [1]. - DVdm (talk) 06:33, 6 July 2020 (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)π, 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)