Talk:Trigonometry

Trigonometry 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, 2009 Good article nominee Not listed
WikiProject Mathematics (Rated B-class, Top-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 B Class
 Top Importance
Field: Geometry
A vital article.
One of the 500 most frequently viewed mathematics articles.
Wikipedia Version 1.0 Editorial Team / Vital

Etymology

"Trikona" in Sanskrit is "Triangle" and precedes the greek word. — Preceding unsigned comment added by 115.184.93.35 (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 121.247.74.93 (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. 75.118.170.35 (talk)

Stop It

This page was really useful two days ago until someone dissected it. Stop breaking it up. 7/21/1p —Preceding unsigned comment added by 174.199.140.153 (talk) 16:06, 21 July 2010 (UTC)

Graph

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

Result: Quick-fail

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.

• 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 71.207.86.13 (talk) 22:13, 21 August 2009 (UTC)

Illustration with law of sines and cosines

Laws of sines and cosines\begin{align} \frac{a}{\sin A} & = \frac{b}{\sin B}=\frac{c}{\sin C} \\[5pt] \cos C & = \frac{a^2+b^2-c^2}{2ab} \end{align}

I seem to be in a disagreement with User:Anonymous Dissident who objects to the formulas in the illustration to the right, saying "It seems redundant to repeat the formulae here, and the omission of the tangent law is a noticeable inconsistency. PNGs in captions can also be unfriendly." I find having the formulas in the caption quite helpful and see no problem with captions repeating information in the text. Rather than get into an edit war, I'd like other opinions.

I also don't understand the reasons for Anonymous Dissident's edits to the intro. Why is the fact that Trigonometry is taught in secondary schools to be mentioned before the fact that it has important applications? And why the objection to the mention that trig is an informal name?--agr (talk) 14:59, 28 October 2009 (UTC)

Redundancy is a bad thing. We are an encyclopedia, and the idea is to be robust. The simplicity of the diagram in question makes it best useful as a simple representation of the configuration discussed in the prose. Readers should be directed to read the text, and images should function as illustrations. The edits to the intro were made only because it disrupted the flow to have a one-sentence third paragraph only on spherical trigonometry. Originally, the bit about school courses was last, but – as you rightly noted – it seemed to indicate that spherical trigonometry is taught in high school. So I changed the order. I removed the mention of "trig" because it's implied by the hatnote, and out of place anyway. —Anonymous DissidentTalk 05:23, 29 October 2009 (UTC)
Print encyclopedias have illustrations and I would expect one very similar to the one on the right to appear in more than one. The version you created, however, is indeed redundant, a very similar diagram appears earlier in the article. We are writing for a general audience, not specialists. Math is hard enough. Diagrams that help our readers should not be deleted out of some sense of purity. And as for "trig," no print encyclopedia would use header information in place of article content. I do like what you did with the animations tho.--agr (talk) 22:22, 29 October 2009 (UTC)
I can't do anything but re-iterate my points above. I suggest both our views are legitimate, and that we should wait for a third opinion. —Anonymous DissidentTalk 06:15, 30 October 2009 (UTC)
Here is my humble opinion. One should avoid repeating information where possible. Since the formulas are located next to the figure, my preference would be to not duplicate the information. Regarding order of information, I would go with chronological order. One learns trig in school, then one uses it in the scientific or business world. So my preference would be to leave the order as is. Regarding the inclusion of the term "trig", that seems reasonable since it is probably used more than the full term itself. I would have no objection including a phase such as "commonly referred to as 'trig' " or some other such phrasing. Just my humble opinion. JackOL31 (talk) 01:58, 19 November 2009 (UTC)

graph mnemonics

Half the mnemonics in the graph with noted ratios are not explained. Maybe it needs a key? —Preceding unsigned comment added by 203.214.158.105 (talk) 06:23, 11 April 2010 (UTC)

Article lacks useful content

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)

SOHCAHTOA

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

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)

Sinθ≠θπ÷180

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 166.214.45.164 (talk) 00:07, 24 September 2010 (UTC)

A definate plus

Adding the polar graph with the trigonometric functions would be a good add. —Preceding unsigned comment added by 166.214.170.106 (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? 75.118.170.35 (talk) 16:18, 21 January 2011 (UTC)

Sanskrit etymology pointless?

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)

Mnemonics

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?

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
56,800 SOHCAHTOA
37,300 AOTAHCOHS
524 OHSAHCOAT
452 TOACAHSOH
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. 74.253.6.205 (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

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:

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 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.
cwm9
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)
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)
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

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)

Parenthesis

OOPS, the edit here of 117.198.245.180  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

Hi,

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

$\tan x = \frac{e^{-ix} - e^{ix}}{i(e^{ix} + e^{-ix})}.$

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 86.88.172.16 (talk) 12:10, 28 September 2013 (UTC)

Note that 1/i = -i and
$\tan x = \frac{e^{ix} - e^{-ix}}{i(e^{ix} + e^{-ix})} = \frac{-i(e^{ix} - e^{-ix})}{e^{ix} + e^{-ix}} = \frac{i(e^{-ix} - e^{ix})}{e^{ix} + e^{-ix}}.$
Hth - DVdm (talk) 14:19, 28 September 2013 (UTC)

"Pythagorean" Identities

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

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)