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Former good article nomineeTrigonometry was a Mathematics good articles nominee, but did not meet the good article criteria at the time. There are 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.
February 23, 2009Good article nomineeNot listed


"Trikona" in Sanskrit is "Triangle" and precedes the greek word. — Preceding unsigned comment added by (talk) 13:19, 22 December 2011 (UTC) Could we add a section on the etymology of the word "trigonometry" here? —Preceding unsigned comment added by (talk) 13:31, 21 December 2010 (UTC)

I don't see how that's necessary
Tri-: three
-gon-: angles
-ometry: measuring
Trigonometry: the measuring of triangles. (talk)

Stop It[edit]

This page was really useful two days ago until someone dissected it. Stop breaking it up. 7/21/1p —Preceding unsigned comment added by (talk) 16:06, 21 July 2010 (UTC)

Merge proposal[edit]

Suggest that this article is merged with "trigonometric functions" Ehrenkater (talk) 15:15, 25 December 2008 (UTC)

Agree with a merge as long as the merged article retains the title of "Trigonometry." :Must assume a layperson looking for information on trigonometry would be looking for "trigonometry" and not "trigonometric functions."
- Brian Lakeman (talk) 15:53, 8 August 2014 (UTC)
This page is under the control of those "laypersons" that Brian Lakemman mention. If it where written by a mathematician, the many errors and misconceptions would not exist.
It is a problem in Wikipedia, that many articles are entered by enthusiast kids, which write what they have in their school notebooks. If not, why should the mnemonics for sin, cos and tan be placed here. Those mnemonics say nothing to not English native speakers. But that is a minor point. Both articles are similar, maybe this has more mistakes. Maybe this article makes more happier those kids which don't understand what is a function beyond those real functions that they see their basic algebra courses.
Apart of merging the articles, this entry deserves a more structured content, written by a mathematician, not by high school students. I opened this article to remind a trigonometric formula, that is absent. But I wont fix it, but I had done it before and there is someone watching for changes and avid to revert anything that is not in their high school notebooks.
Because that is a lost case, I wish success to any brave mathematician that wants to spend a lot of time to write a great article which will be reverted or spoiled in minutes. — Preceding unsigned comment added by 2806:107e:c:1104:218:deff:fe2b:1215 (talkcontribs) 00:42, 28 August 2018 (UTC)


Does anyone have a new version of the sine/cosine (in radians) graph on this page? The two labels overlap. I don't know how to fix this. Quark1005 (talk) 04:59, 12 January 2009 (UTC)

GA Review[edit]

This review is transcluded from Talk:Trigonometry/GA1. The edit link for this section can be used to add comments to the review.

Result: Quick-fail[edit]

This article is not ready for GAN at this time due to non-compliance with quick-fail criterion #1: The article completely lacks reliable sources – see Wikipedia:Verifiability. I notice there are some books referenced in the References section, but they are not incorporated into the body of the article with inline citations. The three sources that are incorporated inline only support minor facts, and one is probably not reliable.

Before this article's next GAN run, here are a few additional issues to consider:

  • The History section is anemic despite having its own article. It's okay to outsource details, but this section does not address the main issues of the topic (GA criterion #3).
  • Per WP:CAP, image captions only end with a period if a complete sentence.
  • MOS:IMAGE should be consulted to ensure that images are placed next to pertinent sections and that no new info is presented in the caption.

Best regards —Eustress talk 14:34, 23 February 2009 (UTC)

It has to do with two thing. —Preceding unsigned comment added by (talk) 22:13, 21 August 2009 (UTC)

Article lacks useful content[edit]

This article has very little content that would be useful to a reader not familiar with the subject. In particular, discussing the laws of sines and cosines without defining what those functions are seem pointless. There were at least some explanations in earlier versions of this article. Why were they cut? Articles are supposed to stand on their own. I'm inclined to restore some of this material.--agr (talk) 01:50, 30 May 2010 (UTC)

You may have seen the article in a vandalized state, someone deleted about half the material and it wasn't restored for 8 hours.--RDBury (talk) 12:51, 30 May 2010 (UTC)
Yup. Shudda looked at the history more carefully.--agr (talk) 16:30, 30 May 2010 (UTC)


I did a Google books search for references on the SOHCAHTOA mnemonic. The word "SOHCAHTOA" turned up hundred of hits, some even in fiction. On the other hand, phrase type mnemonics only came up a few times. This would seem to indicate that the word is much more successful as a mnemonic than any of the phrases and has entered the general culture. The phrases may be clever and amusing but it seems that few are really memorable, a requirement for a mnemonic, and fewer still are encyclopedic. Given this, I'm wondering if the Mnemonics section should be retooled to focus exclusively on the word.--RDBury (talk) 12:46, 30 May 2010 (UTC)

Misuse of sources[edit]

Jagged 85 (talk · contribs) is one of the main contributors to Wikipedia (over 67,000 edits; he's ranked 198 in the number of edits), and practically all of his edits have to do with Islamic science, technology and philosophy. This editor has persistently misused sources here over several years. This editor's contributions are always well provided with citations, but examination of these sources often reveals either a blatant misrepresentation of those sources or a selective interpretation, going beyond any reasonable interpretation of the authors' intent. Please see: Wikipedia:Requests for comment/Jagged 85. That's an old and archived RfC. The point is still valid though, and his contribs need to be doublechecked. I searched the page history, and found 18 edits by Jagged 85 (for example, see this edits). Tobby72 (talk) 20:00, 15 June 2010 (UTC)


I'm trying to figure out how to find the trigonometric functions of angles of non-quadrantal or non-special triangle angles. I came here to see if there was some formula to calculate those. The closest thing I've came up with is Sinθ≠θπ÷180. But the problem with that formula is the Sin1 doesn't 100% true unless you use 3 or 4 significant digits. I know why this is but I can't illustrate that on here. But this is true Sinθ<θπ÷180. π÷180 is 1/360 of a circle and not an straight line up from the y axis thus Sinθ<θπ÷180. If I could illustrate this, it would make a lot more sense. —Preceding unsigned comment added by (talk) 00:07, 24 September 2010 (UTC)

A definate plus[edit]

Adding the polar graph with the trigonometric functions would be a good add. —Preceding unsigned comment added by (talk) 01:32, 10 December 2010 (UTC)


"A common use of mnemonics is to remember facts and relationships in trigonometry. For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, as in *SOH-CAH-TOA:"

Why the asterisk? (talk) 16:18, 21 January 2011 (UTC)

Sanskrit etymology pointless?[edit]

I fail to see how including the Sanskrit word for Triangle-measuring is beneficial...the word was coined from the Greek language by Greek mathematicians...the fact that Sanskrit and Greek both developed from a common language is irrelevant and the similar sound of the word in Sanskrit is a coincidence...can we remove, please? David80 (talk) 12:37, 16 February 2011 (UTC)


You guys have gone over the edge with this mnemonic stuff. You need to keep in mind the target audience for whom you are writing. The goal is not to create an elaborate sand castle to serve as an everlasting monument to your own intellectual superiority.

There is a note in the source code warning others not to engage in "subversive vandalism" by adding a second mnemonic for sine, cosine, tangent--it would be too confusing. And yet we find the three "words" SOHCAHTOA, TOACAHSOH, OHSAHCOAT. Talk about adding "a method of obfuscation ... through a 'learning mnemonic' " [what ever that is]. (And what, pray tell, happened to AOTAHCOHS?? I hope it does not feel left out.)

These nine-letter "words" are not mnemonics--they are just brute force memorization of nine unlinked letters [like a phone number]. They are what mnemonics are designed to avoid. Mnemonics should connect and organize concepts. They should not be too clever--the cleverness will distract from the purpose. They should be short, rather than wordy. Which palindrome is easier to remember?

Madam, I'm Adam.     OR     Able was I, ere I saw Elba.

So, most of all, mnemonics should be memorable. They need to be memorable because they are not in everyday use. They need to be memorable because they must be recalled from the depths of our memory after some period of non-use.

SOHCAHTOA would be great, if it spelled three common words which could be related to each other. Better to make it a cheat-sheet, such as: "S = O/H; C = A/H; T = O/A". Once you put it this way, you can make up a story:

Sine and Cosine were two cousins. Sine Sailed away over the Sea and now lives on the Opposite side of the world. Cosine lives in a Cozy little town that is very Close--in fact it is Adjacent. While Sine and Cosine wear different brands of shirts Over their pants, they both wear the same brand of pants with the odd name of Hypotenuse. Tangent has kept in Touch with both cousins; but Tangent prefers Sine Over Cosine because Sine lives on the Opposite side of the world while Cosine lives in the Adjacent town.

End of story. Simply Complex, Hey? In fact, it would be much easier to remember a short six-word aphorism.

I learned: "Some Old Horses Chew Apples Happily Throughout Old Age" when I was in school. In one ear and out the other. It's too long and a bit contrived. One day, I overheard a kid at the next table in the cafeteria tell a friend the best way to remember sine, cosine, tangent was the sentence: "Otto has a heap of apples." He did not repeat the words; and I did not write them down. I have done very little trigonometry in my adult life. But this mnemonic has stayed with me for 50 years. It is very memorable. It is not "absolutely ridiculous", in the words of this page's unnamed guardian of ideological purity. (I cannot figure out who the censor is as non-printing comments in text do not seem to show up in the history.)

I had previously offered my favorite mnemonic as an alternative to--not a replacement of--the current mnemonic (or plural, if you count those three unpronounceable--and therefor unmemorable--nine-letter "words"). Seemed like an innocent minor edit to me. It was deleted by Gandalf61 with the obscure comment: "rmv random mnemonic". I think what he was upset about the fact that it did not contain any: S-word, C-word, or T-word. Now, let's get real. All mnemonics make assumptions about the knowledge of the users of the mnemonic. This is a mnemonic about sine, cosine, tangent--in what order would they appear in the mnemonic? [If for some perverse reason a user wanted a different order, the user could change the sentence to "A Heap Of Apples, Otto Has", or "Of Apples, Otto Has A Heap", or "Of Apples, A Heap Otto Has", or "A Heap Otto Has, Of Apples", or "Otto Has, Of Apples, A Heap".] The order "sine, cosine, tangent" is found on pocket calculators, in books of trigonometric tables, and on web pages of trig calculators. This order is virtually universal (except for "TOACAHSOH"). Further, the assumption is made that the user knows to use the first letters of the words and understands what those initial letters mean. Finally, it is assumed the user knows how to group the letters and understands the unstated relationship among the letters. If not, the user might think: "Sine + Opposite = Hypotenuse"; or worse yet: "Sine + Opposite = Hypotenuse × Cosine" and "Opposite × Hypotenuse + Tangent = Opposite – Hypotenuse". If reasonable assumptions are not made, then every mnemonic fails because "Results May Vary".

This is not a popularity contest. However, I searched the Internet for mnemonics relating to sine, cosine, tangent. This is what I found:

Hits Mnemonic
107,000 Oscar had a heap of apples
203 Oscar has a heap of apples
6 Oscar has a heap of acorns
1 Oscar had a heap of acorns
8 Oswald has a heap of apples
4 Oliver had a heap of apples
1 Oliver has a heap of apples
3 Ollie had a heap of apples
1 Ollie has a heap of apples
2 Otto had a heap of apples
1 Otto has a heap of apples
2 Olivia had a heap of apples
357 Some Old Horses Chew Apples Happily Throughout Old Age

So, the winner is: "Oscar had a heap of apples"--more than SOHCAHTOA and AOTAHCOHS combined. (Otto didn't do too well. But he is happy his brother Oscar won.) A previous search on this talk page reported much lower results, but the search was limited to Goggle Books. (#3, AOTAHCOHS, is not currently one of the three chosen "words" on this page.)

Do your readers a favor. Scrap SOHCAHTOA, TOACAHSOH, OHSAHCOAT. Too many and too confusing. The mnemonic section should have:

One introductory sentence;
The mnemonic: "Oscar Had, A Heap, Of Apples";
One explanatory sentence;
Three equations showing the ratios for sine, cosine, and tangent (in that order);
One concluding sentence.

Peace and harmony will reign forever.

PS: I'll do it, if you think I can rise to your high intellectual standards, and if everyone promises not to kick me down the street.

Colin.campbell.27 (talk) 20:01, 27 February 2011 (UTC)
I remember SOHCAHTOA as "Some Old Hippie Caught Another Hippie Trippin' On Acid." It's pretty memorable and it makes students laugh. (talk) 15:10, 19 May 2011 (UTC)

If you want to add a new mnemonic, you need to
  1. Establish a consensus that, despite the top note in the mnemonics section, the article will actually benefit from the addition of another mnemonic or the replacement of the current mnemonic. The way to do this is to open a polite and rational discussion here on the article's talk page. Snide remarks about "intellectual superiority" are not going to help your case.
  2. Show that your mnemonic can be referenced to a reliable source, which demonstrates its notability.
Tick both of those boxes, and you are good to go. Gandalf61 (talk) 10:00, 17 June 2011 (UTC)

New mnemonic[edit]

So, maybe I am a bit sensitive since I an new and spent a fair amount of time adding what I thought was a useful contribution, but after adding this edit it was immediately reverted by Gandalf61 (talk · contribs) for the reason: "unsourced, looks like OR, and is too complex to be called a mnemonic". Now, I can understand the unsourced argument a little. The source for the image was my father, and I was unable to find any reference to this mnemonic anywhere. However, the equations which are easily read off of the diagram are all well sourced. See Abramowitz and Stegun, p. 73, 4.3.45 if you really need to. It is easy enough to verify the equations. It's not like it's an opinion. Just look at the diagram, and it either works or it doesn't. (How is "Some Old Hippie Caught Another Hippie Trippin' On Acid" not unsourced original research?)

As to the "it is to complex" argument, the mnemonic itself is a small diagram consisting of the names of the functions and a few lines -- and in exchange for this simple diagram you get back out all of the basic identities. If this really is too complicated, then fine, but it certainly got me through high school and I still remember it to this day, and by that definition I would call it successful. A mnemonic is just a device which is supposed to help you remember. I don't recall there being a limitation on how complex or simple the mnemonic is supposed to be. I also don't know of any other mnemonic which can quickly yield these identities, so it would seem it is this or nothing.

I was under the impression you were supposed to revert only when necessary and not just because you don't like an edit. Otherwise I thought there was supposed to be discussion of the matter. But enough, I am new, and I am not going to waste your (or my) time re-reverting the change. If others find this information useful, whatever process is is supposed to happen can happen. edit: ...though I don't appreciate the text of this being collapsed with the text of the mnemonic where noone can read it.

Here's the text:

Expand here to see mnemonic

Another mnemonic, Chinese in origin, permits all of the basic identities to be read off quickly. Although the word part of the mnemonic used to build the chart does not hold in English, the chart itself is fairly easy to reconstruct with a little thought. (Functions appear on the left, co-functions on the right, a 1 goes in the middle, triangles point down, and the entire drawing looks like a radiation symbol.)

Trigonometric identities mnemonic
Reading across the central 1 in any direction gives reciprocal identities:

Reading down any triangle gives the Standard identities (starting at the top and going clockwise):

Reading a function and dividing the two consecutive clockwise or counter clockwise neighbors gives these identities:

(Starting at Tan and going clockwise)

(Starting at Tan and going counter-clockwise)

Reading a function and multiplying the two nearest neighbors gives these identities (starting at Tan and going clockwise):


The mnemonic is long and has no citation, these are good reasons to revert till a citation is got. You have now confirmed that the source you have is your father rather than any book or magazine or suchlike and I'm afraid that's a killer. Wikipedia has strict rules to ensure that everything in it is something people have actually noted in the real world rather then being editors' own ideas, see WP:Original research. This is to ensure WP:Verifiabiity. It is not up to editors to check out ideas themselves, they only check that somebody else has written about it. Basically something like this really does need a citation. Dmcq (talk) 07:37, 18 June 2011 (UTC)
The question is one of Venerability, and the equations can be easily verified. If you want a reference to the equations, here you go: Abramowitz and Stegun, p. 73, 4.3.45. Why is it OK to include "Some Old Hippy Caught Another Hippy Trippin' On Acid"? Is there a reference for it somewhere? Of course you accept it because the first letter of each word clearly converts to SOH CAH TOA. It's obvious and unchallengable that the conversion is straightforward. It should be obvious to verify this: are you saying you believe the accuracy of the mnemonic is in question? edit: I noticed that there now appears a reference for that sentence, but the reference is not legitimate. The reference itself contains the sentence "Some old horse came a'hopping through our alley," not the sentence referenced.
The only real non-sourceable content here is the diagram itself, but this is nothing unusual. Consider all of the other diagrams in use on the page, such as Image:Circle-trig6.svg Circle-trig6.svg Is there a reference to this diagram somewhere? Was it copied verbatim from a textbook? Was someone credited? No, someone simply drew up this SVG and included it and it was accepted because it is obviously verifiable.
I do not question the claim that the mnemonic diagram did not come from a textbook. I posit that excluding this mnemonic because this fact is being overly pedantic. The fact is that WikiCommons is FREQUENTLY used to upload copyright unencumbered original material for use in Wikipedia -- indeed, isn't that one of the reasons for its existence? Are not the vast majority of images included in Wikipedia technically "original material"? To be consistent, the Hippies sentance should be removed, and the images on the page should be removed until a reference is got.cwm9
I'm not saying it is wrong. I'm simply saying you should read the policies I pointed at. Wikipedia does not publish editors own thoughts. It is supposed to summarize things which have been published in reliable sources. That is what makes things verifiable and notable and not original research. It needs a citation not your personal arguments. Illustrations of things which appear in the article need not be cited provided they are reasonable illustrations and introduce nothing new, examples are the same. Dmcq (talk) 21:34, 18 June 2011 (UTC)
The illustration does not introduce anything new. Is there some new math therom, some equation which needs peer review? You simply look at the diagram and say, yup, those are the equations that every which school student who has ever taken trig has been exposed to, and which can be properly referenced thousands of times over. What opinion needs review by what authority? Does some math Ph.D. need to come along and say, yeah, it looks like that diagram gives the equations we all know are true? Seriously?
The policies state that the goal is to have everything be verifiable and that you can come up with a reference for a claim if one is requested. The policy is not that everything must be a quote or verbatim copy. The example given is "Paris is the capitol of France." It's OK to write "The capitol of France is Paris," or "France has Paris as its capitol," even though it is not a direct quote, because it is verifiable. In this case, the equations are all easily verifiable. How is this not within the stated policies? Again, the image I talked about above is not a verbatim copy from a textbook, yet it is accepted. Why? Because it is unlikely to be challenged and is easily verifiable.
How easy is this to verify? Look at the diagram. Do the equations match what is published in every trig book? Verified!
Here is a list of "unverified" claims currently in the article:
--Trigonometry is usually taught in middle and secondary schools either as a separate course or as part of a precalculus course. Say's who?
--Today scientific calculators have buttons for calculating the main trigonometric functions (sin, cos, tan and sometimes cis) and their inverses. Most allow a choice of angle measurement methods: degrees, radians and, sometimes, grad. (Has anyone done a statistical analysis on how many calculators permit the use of radians and grad?)
--The floating point unit hardware incorporated into the microprocessor chips used in most personal computers have built-in instructions for calculating trigonometric functions. The VIC-20 didn't have them. How do we know this is true?
Of course, these are all absurd cases of "needing references." Requiring them would be overly pedantic.
Yes, you are right, those claims do need sources, and I have added {{Citation needed}} tags to those sentences in the article. The "SOHCAHTOA" mnemonic has a source. The "History" section of the article is an example of a well-sourced section - notice that almost every sentence has a source. This may seem overly pedantic to you, but it is how Wikipedia works. Gandalf61 (talk) 10:23, 19 June 2011 (UTC)
And notice the stuff Gandalf61 stuck citation needed on was small little things that everyone knows about anyway. That was being a bit pedantic under WP:Verifiability and not really needed but yes it does illustrate the level required for Wikipedia. There is no citation for this and it is not generally known by anyone in the business so a citation is needed. This is basic to Wikipedia and you're not going to change it by this sort of argument of a talk page. It is why Wikipedia has got some reputation rather than being a pile of junk akin to all the numerous blogs on the web. Dmcq (talk) 11:40, 19 June 2011 (UTC)
This argument about citing sources is largely irrelevant. The problem with adding a new mnemonic to this article is that this article does not need a longer section on mnemonics. This is the general, top-level article on trigonometry, designed as a broad-level introduction to the subject, and in that context the inclusion of even the SOH-CAH-TOA mnemonic is debatable. If you would like to create a new article Mnemonics in trigonometry with a list of sourced mnemonics that have been used in math education, be my guest. We could include a Main article link to it at the top of the mnemonics section in this article. Jim.belk (talk) 19:04, 19 June 2011 (UTC)
It still should go in without a citation in a special article for such mnemonics so it isn't that minor a point. Dmcq (talk) 21:30, 19 June 2011 (UTC)
The need for citations is certainly not a minor point, but it is not something that needs to be addressed here. The main issue is that this article is not a good place to add this content.
Cwm9, I have gone ahead and created a new article on Mnemonics in trigonometry, which includes most of the material that you wrote. If you're willing, please go there and try to improve the article further. For example, you could try to find a source for the Chinese mnemonic, or you could add some information on other popular mnemonics used in trigonometry. As it currently stands, the article is probably in some danger of deletion, but I think it has the potential to be a good article if you work on it a bit. You may also want to read over the policies at Wikipedia:Verifiability to get a sense of what kind of content Wikipedia is looking for.
By the way, you should try not interpret the reversion of your edit here as hostility. I think the picture that you made is fantastic, and it's great that you're trying to add content to Wikipedia. The main problem is that Trigonometry is major article that needs to function as a concise summary of the field and as a gateway to various sub-articles, which means that this is not the right place for additional content on mnemonics. Also, because this article is already fairly high quality and is relatively well-sourced, editors here are a bit resistant to changes that involve unsourced information. As a new user, you will probably have more success if you start by working on articles that have a slightly lower profile. Jim.belk (talk) 05:56, 20 June 2011 (UTC)
Why have you done this? It is uncited and big and there's no indication anyone has ever used it, Wikipedia is not a blog for people to stick in their bright ideas. I'm not denying it looks okay but it is not Wikipedia's job to publicise new ideas if they haven't been noticed anywhere else. Dmcq (talk) 11:03, 20 June 2011 (UTC)
To the person who stuck that mnemonic in. I'll leave that other article there for the moment with the warning to see if someone else comes up with a citation but if no citation appears it will disappear eventually. There is no point in the arguments about consistency or anything. Wikipedia is not for publicizing ideas no matter how good if they haven't been noticed in a reliable source. Find some leaflet or book or directions from some educational body or anything like that but if you can't find anything it has to go. Dmcq (talk) 11:22, 20 June 2011 (UTC)

Visual mnemonics[edit]

I don't know if this is useful, but I've always used visual mnemonics to remember the sin, cos, and tan relations.

  • the hypotenuse and opposite sides resemble a lowercase cursive "s" (∧), which is suggestive of "sin".
  • the hypotenuse and adjacent sides resemble a "c" (∠), which is suggestive of "cos".
  • the adjacent and opposite sides resemble an inverted "t" (⌋), which is suggestive of "tan".

Would something like this be considered useful for the article? — Loadmaster (talk) 16:40, 8 May 2012 (UTC)

Sources... notability... one favourite mnemonic per contributor... So, probably not, I guess... - DVdm (talk) 17:16, 8 May 2012 (UTC)


@Materialscientist and DVdm: OOPS, the edit here of (talk · contribs · WHOIS) was correct. — Arthur Rubin (talk) 15:20, 21 July 2013 (UTC)

Looks like ip 117 first used the wrong kind of door. Now properly closed :-) - DVdm (talk) 16:17, 21 July 2013 (UTC)

tan(x) in euler notation[edit]


Yesterday I made a change to the formula for tan(x) in euler notation. I believe it should be:

Because tan(x)=sin(x)/cos(x) it can be calculated that the above is correct. If I am wrong, please explain? Thanks — Preceding unsigned comment added by (talk) 12:10, 28 September 2013 (UTC)

Note that 1/i = -i and
Hth - DVdm (talk) 14:19, 28 September 2013 (UTC)

"Pythagorean" Identities[edit]

The article has a subsection called "standard" identities. Should it not be called "Pythagorean" identities? MaximusAlphus (talk) 21:59, 12 January 2014 (UTC)

New animation, explaining sine and cosine as related to the unit circle, with their respective graphs[edit]

Cos, sin and the unit circle.

For what it's worth, I recently made this animation explaining cosine and sine in terms of the unit circle. Please, read the image's description on the image's page (just click the image) before making any remarks.

This is the only representation of both functions and their relation to the unit circle I could figure out that would:

1. Show the graph of both sin(θ) and cos(θ) in the usual orientation, where the horizontal axis represents θ and the vertical the value of the function.

2. The graphs shown, when animated, would not be drawn inverted when θ increases (the point in the unit circle moves counter-clockwise, as usual).

The "bent" way I used to represent cosine was necessary in order to have the graph y = cos(θ) in the usual orientation, condition 1 above, otherwise it would have to be vertical, and users would have to "tilt their heads" in order to see the graph properly. This not only would be very lazy, but it would be a terrible idea because:

  • There would be a huge, empty square between both graphs. The animation frame would be too large, and mostly empty space. This space would not be useful for anything else that wouldn't be conveyed better in the accompanying article or image description.
  • There would be no way to compare both graphs at once.

Therefore, his odd format is justified. Notice that this bend could be done either to the left or to the right. However, if to the right, the graphs would be drawn backwards in the animation, as they would be drawn from the left, and not to the right, as it is currently. This breaks condition 2, mentioned earlier.

I'm not sure if everyone would be OK with including this animation in the article. I couldn't figure where to place it anyway. So, for now, I'm just letting you guys know this animation exists. Cheers! — LucasVB | Talk 16:21, 16 March 2014 (UTC)

Possible copyright problem[edit]

This article has been revised as part of a large-scale clean-up project of multiple article copyright infringement. (See the investigation subpage) Earlier text must not be restored, unless it can be verified to be free of infringement. For legal reasons, Wikipedia cannot accept copyrighted text or images borrowed from other web sites or printed material; such additions must be deleted. Contributors may use sources as a source of information, but not as a source of sentences or phrases. Accordingly, the material may be rewritten, but only if it does not infringe on the copyright of the original or plagiarize from that source. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. Wikipedia takes copyright violations very seriously. Diannaa (talk) 22:47, 28 July 2014 (UTC)

Definition of trigonometry[edit]

Perhaps this is too small a quibble, but I would change the definition in the lede from

relationships involving lengths and angles of triangles


relationships involving lengths and angles of right triangles, and applications thereof.

All the trig functions are defined in terms of specifically right triangles, so that should be in the key part of the definition. Sure, one application of trig is to general triangles via the law of sines etc., but another application is to quadrilaterals and we don't include them in the definition. (talk) 18:19, 29 July 2014 (UTC)

See indeed Trigonometry#Common formulas. and, more importantly, for instance, this and this. - DVdm (talk) 18:29, 29 July 2014 (UTC)

1 for hypotenuse and 90 for the angle that is opposite of the hypotenuse[edit]

edit request for Pythagorean Identities: when x is > or equal to 1 the following examples are true.I don't know if this is original research or not but it states that for all integers bigger than one and equal to one, examples: c,d,e show that the hypotenuse which faces the angle of right angle triangles is one, and 90 degrees for the angle which is opposite of the hypotenuse, and in radian: 90 degrees is . I don't see these examples listed in any article concerning trigonometric functions.






where is a slope and included in (talk) 15:32, 5 September 2014 (UTC)

Not done indeed per wp:NOR. Cheers. - DVdm (talk) 19:10, 5 September 2014 (UTC)

Applications of trigonometry section, goes comically overboard[edit]

I hope that the only reason that "phonetics" was included in this overly-long list is because its own wiki page says that phonetics also deals with sign language. — Preceding unsigned comment added by 2601:8:9200:101:BDFE:DC64:ADAE:C79B (talk) 22:16, 21 February 2015 (UTC)

Please sign your talk page messages with four tildes (~~~~). Thanks.
More likely because in section Phonetics#Subfields we read:
DVdm (talk) 11:00, 22 February 2015 (UTC)

DVdm, mostly, I was just being funny(punny), but I do think the section is much too long. I would particularly want to see the one example which simply states "many physical sciences" removed for obvious reasons. It should be clear to the reader from the rest of the list that ALL physical science is modeled using trig and/or fancier math methods which are built on a solid trig foundation. PS; is this how you want me to sign? (~~~~). or; are there other acceptable ways to sign when not logged-in?, e.g., (RickW). — Preceding unsigned comment added by 2601:8:9200:101:bdfe:dc64:adae:c79b (talkcontribs) 03:10, 24 February 2015 (UTC)

The (only) acceptable way to sign, is by typing four tildes (~~~~), but obviously without the nowiki-tags. - DVdm (talk) 13:13, 24 February 2015 (UTC)

==sin(x) and cos(x)==\\\\sin (x)+cos(x)=1\\\ I have an equation.I know the slope is 4 and I take the which is 16. I add and take the inverse of 17 which is and subtract it from 1 which is the hypotenuse.And I get both opposite side and adjacent side.And by taking the square root of both opposite and adjacent I obtain both correct result without knowing. Therefore I don't need to use.Trenteans123 (talk) 14:38, 16 March 2015 (UTC) =+++==sin^2 (x) +cos^2 (x)=2==|||| atradejas 2006m Marcelius de"Martirosian tel:867752875

Triangle identities[edit]

Everything under the section "Common formulae" (or "Common formulas") is an identity about triangles; I think the section should be called "Triangle identities". I've put in anchors to avoid damaging links, but the section title no sense makes. — Arthur Rubin (talk) 18:23, 12 July 2015 (UTC)

Possible better cover photo[edit]

I think that the space station Canadarm picture may not be a good cover photo to illustrate trigonometry, although it may be used somewhere else in the article.

I recommend something like a graph of trig functions. --Fazbear7891 (talk) 01:40, 18 August 2015 (UTC)

Please put new messages at the bottom. Thanks.
I agree. I'd propose to move this image to the lead:
All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O.
Possibly with a new caption. - DVdm (talk) 08:19, 18 August 2015 (UTC)
Possible cover. but seems very complicated nonono its ok. thanks anyway --Fazbear7891 (talk) 05:06, 19 August 2015 (UTC)
I went ahead ([1]) and moved the canadarm to article Uses of trigonometry ([2]). - DVdm (talk) 08:22, 19 August 2015 (UTC)

List of specific values[edit]

The trigonometric values of 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360° are not given in a systematic table please add that table. Mahusha (talk) 17:18 5 November 2015 (UTC).

It's at List of trigonometric identities#Angles. Should it be here? I really don't think so. — Arthur Rubin (talk) 04:02, 21 November 2015 (UTC)

Semi-protected edit request on 25 April 2017[edit]

pakeitimas :sin^2 A+cos^2=2 redagavo genetikos matmodelio atradejas Marcelius Martirosianas tel: (redacted potential personal details)

2(SIN A+COS A)=2*1=1+1=2 pertvarkuome (talk) 12:33, 25 April 2017 (UTC)

Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format. — IVORK Discuss 12:37, 25 April 2017 (UTC)

Semi-protected edit request on 25 April 2017[edit] (talk) 12:59, 25 April 2017 (UTC)
Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format. — IVORK Discuss 13:38, 25 April 2017 (UTC)

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Semi-protected edit request on 26 August 2017[edit]

Hi, please change

"The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies"

to something along the lines of

while until recently believed to be a Greek invention, trigonometry was actually developed by the Babylonians at least 3700 years ago. this predates Hipparchus, traditionally regarded as the founder of trigonometry, by more than 1,000 years.


many thanks (talk) 06:15, 26 August 2017 (UTC)

Not done The theory proposed by a recent article that is reported on in these news articles has certainly not been accepted by the academic community at this point. Reporting this as accepted fact is too premature.--Bill Cherowitzo (talk) 17:08, 26 August 2017 (UTC)
Dover published a book called: "The Exact Sciences in Antiquity". It has many algorithms from ancient civilizations like Babylonian and Egyptian as the roots of the western civilization.
What about the ancient pre-Colombian civilizations that had advanced astronomy and built amazing pyramids, perfectly aligned to project the shadow of a snake (Quetzalcoatl) during the equinox? The Mayans had mechanic calculators, a 20 base positional numerical system with the use of zero. They could not do that, if they ignored trigonometry. But, nothing is mentioned about maths in non-western cultures.
Shouldn't that be mentioned in this article? if anyone knows about that subject. — Preceding unsigned comment added by (talk) 21:36, 27 August 2018 (UTC)

Possible Update to History Section[edit]

Perhaps the history section should be updated to reflect these new findings:

3,700-year-old Babylonian tablet rewrites the history of maths - and shows the Greeks did not develop trigonometry

The Wikipedia article already says that, "...the Babylonians, studied the ratios of the sides of similar triangles and discovered some properties of these ratios but did not turn that into a systematic method for finding sides and angles of triangles."

The article from The Telegraph says that:

"The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The left-hand edge of the tablet is broken but the researchers believe that there were originally six columns and that the tablet was meant to be completed with 38 rows."

Jjjjjjjjjj (talk) 08:20, 27 August 2017 (UTC)

There's a specific Plimpton 322 article which is linked to from the History of trigonometry article; however, I haven't read the academic paper mentioned in The Telegraph story.
Here is a link to it though with the full text:
Jjjjjjjjjj (talk) 08:33, 27 August 2017 (UTC)
This is newspaper hype, trying to sell newspapers. The paper brings up a new justification for an old theory and certainly doesn't prove anything. See the discussion at Talk:Plimpton 322. --Bill Cherowitzo (talk) 16:32, 27 August 2017 (UTC)

Printed tables[edit]

I seriously doubt that Ptolemy printed trigonometric tables. If he did, the Wiki article on the history of printing will need revision! (talk) 18:48, 8 February 2018 (UTC)

You're right. I've changed it. --Bill Cherowitzo (talk) 02:44, 9 February 2018 (UTC)

where is a vertex in the diagram not an angle[edit]

Many formulas refer to the sin A where Á refers to a vertex in the diagram. For that reason it is necessary to redraw the diagram showing the angles, maybe called or , where the Greek letters denote some angle. — Preceding unsigned comment added by (talk) 21:59, 27 August 2018 (UTC)

Semi-protected edit request on 25 February 2019[edit]

Section Law of sines -> First formula a/sinA ... sinC is written as sirC. Change this to sinC (talk) 09:45, 25 February 2019 (UTC)

 Not done: appears to be a display issue, as the source code is correct. I'm seeing the same thing, but if I zoom in the "n" displays correctly. Roadguy2 (talk) 17:58, 25 February 2019 (UTC)

Main drawing is poor and incorrect.[edit]

How can the main drawing be updated to correctly and fully explain the subject? I've tried changing it but some folks keep changing it back to the incorrect image. The current drawing has cosine shown incorrectly and does a very poor job explaining the subject.

This image is correct.

Your new image has a font size so small that the labels are completely illegible when the image is shown in the article. It isn't an improvement. - MrOllie (talk) 17:18, 2 July 2019 (UTC)
That's because their are many functions that need to be correctly and precisely labled. The current drawing lables cosine incorrectly and that seems like a huge problem. --Pvd (talk) 17:21, 2 July 2019 (UTC)
The details here are actually important. A poor drawing that is incorrectly labled isn't a help for anyone. A simple click expands the drawing.--Pvd (talk) 17:23, 2 July 2019 (UTC)
Aha. If size and clarity were the issue, I fixed that so that the image is large enough to be clear. — Preceding unsigned comment added by Pvd (talkcontribs) 18:01, 2 July 2019 (UTC)
No, a giant image that takes up the whole width of the article isn't any good either. What exactly is wrong with the old image? The cosine label looks correct to me. - MrOllie (talk) 18:03, 2 July 2019 (UTC)
@Pvd: I don't see anything wrong with the current drawing:
What do you think is wrong with the cosine? - DVdm (talk) 18:05, 2 July 2019 (UTC)
Look at the image I tried to put up. The cosine can't be on the non-complemetary side. Ugh. This is fundemental.--Pvd (talk) 18:06, 2 July 2019 (UTC)
The original image is terrible and incorrectly labled. Don't like my image? Make a better one.--Pvd (talk) 18:07, 2 July 2019 (UTC)
Please indent your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.
The cosine as the projection of the radius onto the horizontal axis is pretty correct, as you can see in any elementary book. - DVdm (talk) 18:10, 2 July 2019 (UTC)
(edit conflict):What is incorrect in the image? The only issue that I can see is that some very exotic functions that nobody uses do not appear in this figure. As nobody care of them, they may appear in the body of the article, but not in the lead, where the figure is placed (see MOS:LEAD and MOS:MATH#Introduction). In any case, it would be clearer and less confusing to have a figure with only the six most common trigonometric functions, and to move the present figure to the body of the article. D.Lazard (talk) 18:12, 2 July 2019 (UTC)
No. That is incorrect. Please refer to the image that I put up. Neither the cosine or sine are projections onto an axis. The cosine needs to be on the complementary side. This is fundamental to the entire concept of trigonometry. Please study the image I posted. --Pvd (talk) 18:14, 2 July 2019 (UTC)
Please indent your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages.
Please refer to any book on trigonometry. - DVdm (talk) 18:16, 2 July 2019 (UTC)
Please, provide reliable sources for your assertions. Your opinion and your drawing are not reliable sources, and this is an encyclopedia that must be based on reliable sources. D.Lazard (talk) 18:19, 2 July 2019 (UTC)
I don't think you understand this topic. Please try to understand what I've shown. --Pvd (talk) 18:20, 2 July 2019 (UTC)
We understand you, we just don't agree. Can you provide some source that the cosine must not be drawn on the axis? - MrOllie (talk) 18:21, 2 July 2019 (UTC)
The cosine cannot be located on the x-axis as the x-axis is not on the complementary side of the radius. This is as obvious as 2+2=4. Please try to understand this topic and what is going on with the construction. It should be obvious.--Pvd (talk) 18:26, 2 July 2019 (UTC)
Please indent your talk page messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages.
The literature disagrees with you. See, for instance, [3], [4], [5]. Cosine is drawn on the axis. - DVdm (talk) 18:30, 2 July 2019 (UTC)
This is what happens when you don't understand trigonometry. Anyone with a basic understanding of trigonometry understands that those graphics were drawn in error. Citing sources that are wrong is just lunacy. I give up. The clowns have taken over the circus. — Preceding unsigned comment added by Pvd (talkcontribs) 21:54, 2 July 2019 (UTC)
What seems obvious to me is the length of the cosine is the same, regardless of whether you draw it on the x-axis or above it. They're just opposite sides of a rectangle. Highway 89 (talk) 19:58, 3 July 2019 (UTC)
So you've invented a function on the non-coplementary side of the point, but named it the same as a function on the complementary side. That doesn't sound obvious. What is this function the complement of and how does it relate to the point? --Pvd (talk) 22:09, 3 July 2019 (UTC)

See, for instance:

  • [6]: "In the unit circle the values of the cosine and the sine, respectively, of an angle φ are represented as the signed numerical values of the abscissa and ordinate of the radius in the direction of the free arm of the angle φ. The two segments are the orthogonal projections of the radius on the x- and y-axes".
  • [7]: "... the length AN = cos A. This is the projection of P onto the x-axis"
  • [8]: see figure 3-8: "... Ax = A cos θ"
  • [9]: see figure 2
  • [10]: see figures 3-8, 3-9
  • [11]: see figure 6-27
  • [12]: see some more figures

So no, that is not what we have invented. It is what the literature has invented. - DVdm (talk) 07:51, 4 July 2019 (UTC)


was this article locked?, pls put the padlock to let us know or User:Brirush, thank you.

Where are the Indian mathematicians?[edit]

I believe India has it's own history of trigonometry that can be traced back much before the hellenistic world discovered it. Trigonometry originated in India. Can anyone please confirm my point here? Uddhav9 (talk) 08:25, 8 August 2020 (UTC)

If you can provide a reliable source supporting this, you may update section History. Otherwise, you cannot, as it is a basis policy of WP of not including any information that is not supported by a reliable source. D.Lazard (talk) 09:04, 8 August 2020 (UTC)