Talk:Trigonometry/Archive 1

Initialization

I put this together kinda off the top of my head. I think it still needs some discussion of stuff like Law of Sines, Law of Cosines and identities, and maybe a little bit on radian measure, unit circle stuff, whatever. -- Blain —Preceding comment added 15:43, February 25, 2002

That's all covered in Trigonometric_function. —Preceding unsigned comment added by Al-khowarizmi (talk • contribs) 10:24, March 14, 2004 (UTC)

sir, your article is quite good.as you have made hyperlinks to articles related to the term,it explains everything.i have used it for my IGCSE math test,and it is quite good.thank you. —Preceding unsigned comment added by Rudrakshmk pws (talk • contribs) 07:16, October 4, 2005 (UTC)

Rational Trigonometry

New Trig has been discovered. Check out his site for more info I think that this needs to be addressed. —Preceding unsigned comment added by 69.227.151.150 (talk • contribs) 20:16, September 17, 2005 (UTC)

Yeap, and check here [1]

—Preceding unsigned comment added by 83.24.222.224 (talk • contribs) 10:03, September 20, 2005 (UTC)

It's not clear that rational trigonometry merits a comment on this highly selective page. What would seem suitable is a "see also" link with an even briefer description. A more serious problem is that the article on rational trigonometry is not helpful in its present form. But one may still link to it in the hope that its problems will be addressed. Abu Amaal 18:20, 11 April 2006 (UTC)

Meh, i like the memories :-) ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 22:52, 14 May 2007 (UTC)

Mnemonics

I just did some addition to the mnemonics topic. I am just a student so please check up the language and grammar --Nikhil —The preceding unsigned comment was added by 203.101.28.5 (talk) 10:59, 6 December 2006 (UTC).

I do not suggest mnemonics because that messed me up. You made me half forget what they are. why don't people just remember sine=opposite/hypotenuse cosine=adjacent/hypotenuse tangent=opposite/adjacent. Its very easy to remember. InternationalEducation —The preceding comment was added 00:17, January 1, 2007 (UTC).

This section is terrible - far too many mnemonics, some of them highly inappropriate for an encyclopedia - I've removed the whole thing. SOHCAHTOA is by far the easiest way to remember and everything else is both useless and trivial. Richard001 00:37, 4 February 2007 (UTC)

Hmm, I'm a student and well you know, it's easier without the mnemonics. that SOHTAH whatever thing messes me up real bad. More words to remember so that really isn't a mnemonic. InternationalEducation 10:46 Mar 2007

Surely it's worth mentioning, as many people do use the mnemonics? I mean, it's not forcing people to use them any more than reading an article about Hitler will turn them into Nazis. Also, whatever you do to it - please don't remove the "Big Legged Woman" quote, that just made my (sad little) day. 86.144.97.106 (talk) 21:32, 13 January 2009 (UTC)

Definition of Sine and Cosine

I would like to propose the following change: Define sine and cosine via the unit circle. This is much better because it gives sine and cosine directly for all angles. Moreover, this is somehow the main points that sets trigonometry apart from Euclidean geometry: namely that trig functions have signs. They are not ratios of lengths of line segments. The unit circle definition comes much closer to the true nature of the trig functions. It is also much simpler. Any opinions on this? --345Kai 18:28, 13 April 2006 (UTC)

The unit circle definition is much better. I don't agree that its simpler, however. I would have a right triangle section and then a unit circle section. I do think, though, that the unit circle definition needs to be included. --Mets501^talk 20:06, 13 April 2006 (UTC)

I have started writing an alternative version using the unit circle. I propose to first give the definition of the trig functions using the unit circle, and then derive/explain how the trig functions are useful in right triangles, and how it all relates to the theory of similar triangles. Let me know what you think. --345Kai 23:04, 14 April 2006 (UTC)

I like this version much better than what we have. I think it's a big mistake (albeit a common one) to describe trig first-off as 'a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees'. It's so much more than that. I think it's altogether rather peculiar when people take the approach of saying 'this is the maths used to describe right-angled triangles, here are all the ways it does that, just in case you ever need to mathematically describe right-angled triangles for some reason. Oh yeah... and it also happens to describe points on circles and the behaviour of waves, and turns up in a fundamental role all over physics and sound engineering, and in many other seemingly disaparate branches of mathematics. --Oolong 14:33, 27 January 2007 (UTC)

Trigonometry is fundamentally about triangles - historically and linguistically. The trigonometric functions sin(x) etc., however, are ubiquitous in math, and are defined in terms of the unit functions, as generalizations from the trigonometric ratios sinA etc. used in trigonometry.--Niels Ø (noe) 16:02, 27 January 2007 (UTC)

just in case you ever need to mathematically describe right-angled triangles for some reason. For most people, this is the most useful bit of trigonometry. I have often made use of it in my everyday life. How can you not? Skittle 22:18, 14 May 2007 (UTC)

What exactly am I looking for on that page? sorry. (Eventualengineer (talk) 13:10, 25 April 2008 (UTC))

Which page?  --Lambiam 19:43, 27 April 2008 (UTC)

Oops, I accidently put my first question in the topic below but what it was, was Can someone explain how to calculate sine and cosine? I know the sin(theta)=a/c equation.(Eventualengineer (talk) 20:06, 27 April 2008 (UTC))

See Trigonometric function#Computation. For small arguments, you can also use a Taylor series, and larger arguments can be made smaller by using various trigonometric identities such as reflection and halving or doubling formulas. For future references, such questions are better asked at Wikipedia:Reference desk/Mathematics.  --Lambiam 11:41, 29 April 2008 (UTC)

Thanks, it really helped! (Eventualengineer (talk) 18:43, 1 May 2008 (UTC))

Lagadha & trigonometry

From the text:

Indian mathematicians were the pioneers of variable computations algebra for use in astronomical calculations along with trigonometry. Lagadha is the only known mathematician today to have used geometry and trigonometry for astronomy in his book Vedanga Jyotisha, much of whose works were destroyed by foreign invaders of India.

This passage caught my attention at first because of its lack of fluency (e.g., by "variable computations algebra" did the editor mean "variable computations otherwise known as algebra", or "variable computations and algebra"?), but as I pondered these words, I couldn't help but suspect the validity of the claim that Lagadha is "the only known mathematician today to have used geometry and trigonometry for astronomy". This is quite the sweeping statement -- did the editor mean to say that not even modern astronomers use trig? -- & the claim that much of his works were destroyed leads me to suspect that this claim cannot be substantiated. The article on Lagadha is a brief stub & offers no help to determine whether this statement is true or false.

Can someone provide citations for this statement (I suspect it may be true that Lagadha used some kind of mathematical process which is similar in some ways to trigonometry)? This statement is the sole contribution of an editor from an IP address, so I can't evaluate it on that grounds. If it cannot be verified, then it would be for it to be removed. -- llywrch 19:46, 13 December 2005 (UTC)

Links

Any particular rationale for the two links listed? They're not what I'd have chosen...

(but then, I can seldom make sense of which links Wikipedia ends up including)

--Oolong 13:37, 21 February 2006 (UTC)

...of course, what I was really getting at was 'why isn't *my* page about trigonometry listed? The collection of links there are now are much better than the ones from when I posted the comment above though, so I don't mind so much any more. :) --Oolong (talk) 00:27, 27 January 2009 (UTC)

Written in "Wales"?

Please excuse my ignorance, but I noticed this entry in the page and was a little confused that it didn't somehow qualify the location of Wales. Welsh mathematics is something I know nothing about - perhaps it was a mis-spelling of another location:

"The earliest use of sine appears in the Sulba Sutras written in Wales between 800 BC and 500 BC, which correctly computes the sine of π/4 (45°) as 1/√2 in a procedure for circling the square (the opposite of squaring the circle)."

Could someone qualify which "Wales" or else clear this up? —Preceding unsigned comment added by 83.237.174.194 (talk • contribs) 19:17, April 11, 2006 (UTC)

Obvoiusly Wales is not correct, so looked for more details and found none. I changed it to India.

--MathMan64 19:53, 12 April 2006 (UTC)

Proof section

The proofs are not written correctly. You cannot prove that sin^2(A)+cos^2(A)=1 by starting with that equation. While the proofs have the right general idea, they need to be written in reverse, essentially. I am not familiar with the symbolic writing on here, so if someone could do that I would be very thankful. The proofs should be, generally, as follows (taking first Pythagorean identity as example): sin^2(A)+cos^2(A)=opp^2/hyp^2 + adj^2/hyp^2=1/hyp^2 x (opp^2 + adj^2)=1/hyp^2 x (hyp^2)=hyp^2/hyp^2=1. My apologies for the sloppy notation. Please consider this and then make the changes. Thanks. Makeemlighter 05:13, 21 May 2006 (UTC)

I wanted to get to this so thank you for covering this up, but you left out the rest of them.... I don't want to write the equations out, but I can teach you a way to know the origin of the equations. a^2+b^2=c^2 = adj^2+opp^2=hyp^2

adj^2/hyp^2+opp^2/hyp^2=1 since you divide hyp^2 to both sides. adj/hyp=cos so cos^2= adj^2/hyp^2 opp/hyp= sin so sin^2= opp^2/hyp^2 If you subtract the c^2 to the other side and and add b^2 to the other side. You divide b^2 to all of them and you get another equation then you start from the original equation and do the same to a^2. The pythagorean identities are simply equation gotten through plain algebra and a^2+b^2=c^2. —Preceding unsigned comment added by InternationalEducation (talk • contribs) 00:35, January 1, 2007 (UTC)

Reasons for not promoting as a good article

This is a well-written article, but it does not include a single reference. As such it cannot become a good article. However the work required to make this article a good article is minimal. The article really only needs three references: one for the history section, one for the comment on rational trignometry and one for the basic trignometric claims.

A reference for the history can be found on Google [2], the rational trignometry can also be found on Google and the basic trignometric claims can be referenced using a good textbook on the subject.

Once this is done please feel free to resubmit the article for promotion.

Cedars 10:33, 23 May 2006 (UTC)

Rational trigonometry

Someone said this is "new" and ascribed it to an apparently living Australian mathematician. Of course that is utter nonsense, since rational trignometry was well known to the ancient Greeks! Not surprising since they tried hard to reduce everything to computations with rational numbers! See for example, stereographic projection and Euclid's rationally parametrized enumeration of Pythagorean triples. ---CH 22:51, 27 May 2006 (UTC)

Rational trigionometry refers to a specific attempt to make all trigonometry into rational numbers, not the idea that regular trigonometry (the one we use now) consists of rational numbers. —Mets501^talk 22:57, 27 May 2006 (UTC)

Merge

Would it be appropriate to merge this article with the one on trigonometric functions? They'd both be a part of this page, headed "Trigonometry," as it's the broader of the two. The reason for this is I think that the "trigonometric function" article has been used to cover all of trigonometry, and thus what we have on this page ("Trigonometry") is redundant (and in fact, less detailed). Trigonometry is defined by its functions (sine, cosine, tangent, etc.), so I don't think they deserve their own article. In terms of the COTW, porting the information from the "trigonometric functions" article to here (+ incorporating the extra information that shows up on this article and not that one) would save a lot of work; that article takes a good approach to the whole of trigonometry, and would be appropriate under the heading "Trigonometry". James Somers 15:19, 11 July 2006 (UTC)

Well, That's really difficult to decide whether Trigonometry function to merge into Trigonometry because if I Moved Trigonometry function into Trigonometry', that's too much for reading, editing the article. Basically, the size of article can be less 81 kilobytes long. So, Trigonometry function is just different kinds of equations by using Trigonometric functions, but Trigonometry is just explanation about history of Trigonometry. Anyways, That's good idea to port informations from the Trigonometric Functions to Trigonometry. *~Daniel~* ☎ 02:50, 18 July 2006 (UTC)

Origins/History

Someone claims in the article that trigonometry has origins in Egypt etc... but they don't explain what they mean by that, and they don't cite any references. This part should either be removed as unsubstantiated or explained in what way the Egyptians contributed to Trigonometry. —Preceding unsigned comment added by JettaMann (talk • contribs) 17:47, October 5, 2006 (UTC)

Organization

What, exactly, is the purpose of the "About trigonometry" section? Melchoir 23:25, 23 October 2006 (UTC)

I've merged it into the overview section and added some images. Also made a number of other changes, based, in part, on comments from a previous editor on my talk page, q.v. --agr 14:14, 25 October 2006 (UTC)

History

Can someone include the works of Arab and Persian mathematicians Abu 'l Wafa and Ibn Yunus in more detail please, as their contributions are one of the most important in Trigonometry to date. —Preceding unsigned comment added by 146.87.193.90 (talk • contribs) 14:20, October 25, 2006 (UTC)

Can you supply some references or more info? I've added a disputed tag to the section.--agr 14:21, 25 October 2006 (UTC)

Abu 'l Wafa http://en.wikipedia.org/wiki/Abu_%27l_Wafa

Ibn Yunus http://en.wikipedia.org/wiki/Ibn_Yunus —Preceding unsigned comment added by 146.87.193.90 (talk • contribs) 14:23, October 25, 2006 (UTC)

I added them and took off the tag. Do you have further problems with the text?--agr 14:58, 25 October 2006 (UTC)

The early history section has several problems.

• Irrelevant detail (e.g., the grade of a reservoir in Sri Lanka). I am rm these.
• "Time-speak" (omitting the word "the" in phrases like "The Indian mathematician Bhaskara").
• Lack of citation. There are many confident assertions that seem on their face to be uncertain.
• Lack of proportion. It seems there was a surge of additions about South Asian ancient trigonometry, but it is not matched by equivalent detail about other contributions such as those of pre-Classical and Classical mathematicians (e.g., Egypt, Babylon, Greece, Rome). Either there should be more detail systematically, or there should be less. I propose less, and that someone with expertise write a separate article on the (early) history. Meanwhile, I am shortening this section.
• Confused writing. E.g., what is meant by "variable computations algebra"?

I would appreciate it if someone with scholarly knowledge and a sense of proportion would fix these problems. If not, I may shorten this material. Zaslav 12:04, 26 October 2006 (UTC)

Introduction

I don't like this sentence 'Trigonometry is usually taught in U.S. secondary schools, often in a precalculus course.' To me it sounds as if, in order to learn to trigonometry, you have to go, specifically, to a U.S. secondary school. I know this not to be true as I learnt calculus in an English secondary school. - To all those who don't get jokes I know what the sentence is suposed to mean but it is ambiguous. Algebra man 20:08, 25 December 2006 (UTC)

Good catch. I took out "U.S." I hope it is not too broad a claim this way. --agr 04:53, 26 December 2006 (UTC)

Formula for law of cosines

I have pretty much always seen this written, equivalently, as: c^2=a^2+b^2-2*a*b*cos(theta), with a note that theta is the angle opposite side c. This form is more obviously reducible to the familiar Pythagorean identity when theta measures 90 degrees (i.e. cos(theta)=0). Is there any particular reason it was written like it was? —The preceding unsigned comment was added by 64.26.98.33 (talk) 23:33, 27 December 2006 (UTC).

Wow, HagermanBot is quick. I misread, skipping the form I advocated and going to the larger print version I was questioning. Still, is there any reason for using that particular form? Also, the form I mentioned seems to be text, and not a pretty formula like the others. 64.26.98.33 23:38, 27 December 2006 (UTC)

Disagreement with history of math page

The history of math page, under Babylonian history, refers to Babylonian tablets dated around 1500 BC that had trig tables. But the trig page itself, under history, says earliest recorded info on trig was much later. Shouldn't there be agreement between these two pages? —Preceding unsigned comment added by MontyPh (talk • contribs) 22:55, January 2, 2007 (UTC)

SAH something TOA?

What's that formula for you if you want to find out which to use? Something SAH TOA and C..... RollEXE 05:20, 15 February 2007 (UTC)

Well, ya know. The formulas are actually quite easy to remember. Sine=opp/hyp Cosine=adj/hyp Tangent=opp/adj=cosine/sine>>simplified version of all formulas: Sin=opp/hyp Cos=adj/hyp Tan=opp/adj=Sin/Cos Reciprocal Functions: Cosecant:1/sin Secant:1/Cos Cot: 1/tan Just To Let You know Section: sin(π/2-A)=cosA cos(π/2-A)=sinA Law of cosines: c^2=a^2+b^2-2abcosC Now, if you look at this formula. The C in cosC is the the opposite of the side C, so it doesn't matter whether side it is; plug in the the value to the formula and you'll find your side. Law of Sines: SinA/a=SinB/b=SinC/c this is true for all triangles and the angle A for sin A is directly the opposite of side a and so on for b and c. There's actually a way to find the degrees of an angle if you know the value of the cos or sin or tan of whatever the degrees is. For instance, sin X= 0.5 sin^-1(0.5)*=X X is 60 if you flugged in Sin-1(0.5)* Note-The star is the degrees sign and remember to add it. Otherwise the value is measured in radians. Well, you should learn this before its to late and its not really that hard. I couldn't memorize it during fifth grade, but guess what, its becoming easier to to learn. (Yeah I bought a trig book during fifth grade although I knew I couldn't read it. But I learned the first 1/10 by 6th grade hehe. The book name is Trigonometry The Easy Way, highly recommended book. It give you a story to entertain you while learning. Life and death situations in the book. There's also a guaranteed section that you'll IMPROVE your grades after 30 days. If not you can return for full fund. Might be true or not, but'll definitely help you out RollEXE.) InternationalEducation —Preceding comment added 02:42, March 13, 2007 (UTC)

Proposed link

My students have had great success with my Precalculus course notes, particularly the sections on graphing trig functions. Unfortunately, I believe the "Precalculus" article is barely maintained by anybody, though I have suggested my link to that and to the "Algebra" article. Would anyone be interested in posting an external link to them? http://www.kkuniyuk.com/Notes Thanks! (Sorry for my earlier link; I'm a new user) Ken Kuniyuki 00:40, 1 April 2007 (UTC)

Slight inconsistency

The introduction says the name Trigonometry is derived from "Trigona" and "Metron", yet the reference says "Metro" for measure.

"branch of mathematics that deals with relations between sides and angles of triangles," 1614, from Mod.L. trigonometria (Barthelemi Pitiscus, 1595), from Gk. trigonon "triangle" (from tri- "three" + gonia "angle;" see knee) + metron "a measure" "

♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 13:09, 9 April 2007 (UTC)

When I checked the page, someone was claiming that trigonometry comes from Sanskrit. The word definitely comes from Greek. Sanskrit may have had a similar word (I don't know myself) but "trigonometry" is a direct transliteration of several Greek words. The source you cited seems to be the Online Etymology Dictionary. "Tri" means three, "gon" means angle, or more precisely "joint" (hence "knee"), and metron is a noun meaning "measure." The "-on" at the end of the word is a neuter ending for Greek, and it usually falls off of words when they become English cognates, i.e. English-ized. Pay the discrepency in spelling no mind. - RTB, 25 June 2008 —Preceding unsigned comment added by 69.244.214.16 (talk) 22:56, 25 June 2008 (UTC)

Another slightly primitive usage?

I've never really heard the phrase "leg" used as anything other than an elementary uses; the name "sinus" comes from the latin, "bosom", which was with relation to the components of an archer's bow. Any chance we can reference some of this, because these are niggly little bits. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 09:13, 7 May 2007 (UTC)

DO NOT add stupid mnemonics, the section should really exist in the main text in context

I am leaving notice here to those who added the "Sex on.." and "Shit on hippies", etc. DO NOT ADD SUCH nonsensical mnemonics as they are vandalism even if you think they are contributions. They do not attribute anything other than stupidity to the article; the SOHCAHTOA one is fine. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 21:54, 14 May 2007 (UTC)

Hardly Vandalism. What_wikipedia_is_not#Wikipedia_is_not_censored and...Your opinions: What_wikipedia_is_not#Wikipedia_is_not_a_soapbox --CylonSix 16:25, 9 November 2007 (UTC)

Suggested article structure

Because trigonometry is MUCH MORE than just that listed on here at the moment, I recommend that the following article structure be considered; please add comments below.

1. Sexagesimal and circular measure relating to trigonometry.
2. Definitions and introductions to the trigonometric functions with inclusion of the CORRECT derivations and definitions (abscissa and ordinate) and their relation with eachother to the same angle.
3. Trigonometric functions applied to variable angles, and other angles or illustration (30^o -> 60^o ... etc)
4. Inverse functions (for more than one angle)
5. Trigonometric equations, elimination and submultiple (and multiple) angles.
6. Logarithmic relation (Quadrilateral and regular polygons)
7. Explain how earlier in times, people used sin/cos/tan tables! (The time when Geometry guy and I walked the earth)

♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 08:13, 20 May 2007 (UTC)

Considering the article's intended audience, maybe there should be a quick list of variables or another pic like at the begining of the article to avoid confusion about what the identities mean--Cronholm144 00:13, 21 May 2007 (UTC)

I have a problem with introducing terminology like abscissa and ordinate which are not generally taught in schools today. We should not be making this article more opaque. Also, we have an article on angle that goes into different ways of measuring them and I don't think we should reproduce that here.--agr 00:22, 21 May 2007 (UTC)

Well, there's not a problem because they are original terminology used; their use can easily be explained alongside the article and the reason WHY they were called thus was also important in trigonometric development. Secant, cosecant and cotangent aren't taught in schools either, but that doesn't mean they should be excluded because they have been neglected elsewhere. Also , i agree with cronholm. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 08:24, 21 May 2007 (UTC)

It's ok to mention the obsolete terminology later in the article, but the body of the article should use modern language that its audience has been taught.--agr 12:50, 21 May 2007 (UTC)

I can't see any way that sexagesimal measure relates to trigonometry... Paul Koning 16:34, 21 May 2007 (UTC)

I thought it'd be notable to explain the sexagesimal measure as it deals with sub-divisions of a right-angle? ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 17:02, 21 May 2007 (UTC)

I don't think that is the best way to explain it. The sexagesimal system is a Babylonian holdover, and it probably is better described starting from the full circle (360 degrees) since at least that's a multiple of 60. In any case, though, it doesn't have any obvious connection to trigonometry, because that talks about ratios of sides in right triangles, so it is independent of what units or method of measurement you use for the sides (never mind the angles). Paul Koning 17:53, 21 May 2007 (UTC)

A fair point; still, maybe a slight reference to it as a means of showing other methods of measurement would be a good idea? ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 10:38, 24 May 2007 (UTC)

I might help if you describe what you want to add in more detail here. --agr 01:43, 25 May 2007 (UTC)

I wanted to reach that via consensus. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 16:26, 27 May 2007 (UTC)

That's fine, but I really am not clear as to what you are proposing. --agr 22:03, 27 May 2007 (UTC)

Manipulatives

Is this bit missing something? It says.... "To easily remember the sine and cosine functions of special angles, just use your hand. Trace your left hand, and label the fingers as in the figure at right. To find the cosine of 30 degrees, lift the 30 degree finger."

I'm assuming the diagram is missing or it just makes no sense. 130.88.9.78 13:36, 11 July 2007 (UTC)RichMo

I removed the section and replaced it with something I think is more useful (with one oops which annon. kindly corrected). --agr 20:27, 11 July 2007 (UTC)

TrigWorks

I was attempting to add an external link on 9 Aug, 2007, but it was removed by User Kl4m and I was informed that I really should be checking with you before doing that. I noticed that there were some books listed there and so I did not think that another educational item like the TrigRuler would present a problem, but that will be your decision. Please visit my website at www.trigworks.com to see the TrigRuler. I believe that it will be very helpful for many students new to the subject. When I created my account here on wikipedia, I used the name TrigWorks and I guess that is how you can reach me but i have not set up a user page yet, or try me at info@trigworks.com. Thank you for considering this external link. —Preceding unsigned comment added by TrigWorks (talk • contribs) 06:10, August 10, 2007 (UTC)

Wikipedia policy does not normally allow "Links to sites that primarily exist to sell products or services." (WP:EL) The books listed include full downloadable text. Your product may have great educational value and I wish you well with it, but so do may others and Wikipedia is not a product directory. sorry.--agr 13:23, 10 August 2007 (UTC)

??Miscellaneous trig identities??

I have two problems with this section - first of all, the list of identities in the trig article is supposed to use commonly used trig identities, all of which fit into any of the other categories. Second, the one identity listed under "miscellaneous" is wrong, as it returns values of cosine greater than and less than 1, which is impossible. Would anyone care horribly if I deleted that section?

Quodfui 22:08, 4 September 2007 (UTC)

Image dissection

Umm.. Like.. Just looking at this image.. what is versin meant to be?

This image is really overloaded. It cannot be used with confidence by anyone not already familiar with the subject. It should really be broken up into seven separate images, each showing a single function. The simpler images could be accessible, at the least, from thumbnails on the current image, as well as from more specific articles (e.g. sine wave). I'd make the series of simpler images myself (it can easily be edited in Inkscape, which is open source), but it confuses the hell out of me. —Pengo 02:46, 25 October 2007 (UTC)

Each label in the diagram corresponds to the nearest line segment and vice versa; additionally, the colours also relate the various labels to the corresponding line segments. I'm not sure what you feel is not clear. Of course, if you don't know what a trigonometric function is, you won't learn that by just looking at the diagram, but assuming that you know sin and cos and how they relate to the projections of a point on the unit circle to the axes, you should be able to deduce the meaning of versin from the diagram.  --Lambiam 15:55, 25 October 2007 (UTC)

A section on Trig's application to physics

I will be adding a short section on this if you guys approve. It should consist of how motion gets split relative to an incline's known angle. Please add some suggestions here. Also the section will include an upgraded version of this image. Do not expect this to be complete within the next few weeks though.-- Penubag  01:34, 6 December 2007 (UTC)

A couple of things missing

There are a few of basic things that I think should be in the article, the question is where best to put them. We should explain that each "co" function is the function applied to the compliment of the angle. Also we should exhibit basic formulae like cos (x) = sin (90°-x), csc (x) = 1/sin (x) and sin(arcsin(x)) = x, either in the overview or the Common formulae section. We might also mention that tan, cot, sec and csc are not defined or infinite when the denominator is zero. --agr (talk) 12:46, 22 January 2008 (UTC)

Rule of quarters

The article has a section called "Rule of quarters",

The rule of quarters makes it easy to remember the sine function of special angles:

followed by fomulae for sin 0^o, 30^o, 45^o, 60^o and 90^o. I like these formulae, but

1. Are they commonly known under this name? (Try google!)
2. Are they truly a help for remembering? You need to remember several things before you can use them: That it's sines, not cosines; an equation like $\sin A_{n}={\sqrt {\frac {n}{4}}}$ (at least the expression ${\sqrt {\frac {n}{4}}}$); the angles are A₀=0^o, A₁=30^o, A₂=45^o, A₃=60^o, A₄=90^o (a rather odd sequence).
3. Are they not more an oddity, a mathematical coincidence, than something belonging in an encyclopaedic article on trigonometry?

--Noe (talk) 13:03, 28 February 2008 (UTC)

Confused

Hey I'm a bit confused, I can calculate sin and cos by using the formula sin(theta)= a/c but how can you figure it out mathematically(Eventualengineer (talk) 13:03, 25 April 2008 (UTC))

See Trigonometric function#Computation. For small arguments, you can also use a Taylor series, and larger arguments can be made smaller by using various trigonometric identities such as reflection and halving or doubling formulas. For future references, such questions are better asked at Wikipedia:Reference desk/Mathematics.  --Lambiam 11:43, 29 April 2008 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Trigonometry/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Trigonometric function is better. Salix alba (talk) 17:06, 3 September 2006 (UTC) Disagree, trigonometry has far further uses, applications and subject matter than just the trigonometric functions. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ slurp me! 21:58, 14 May 2007 (UTC) (It is a featured article. Geometry guy 12:26, 15 April 2007 (UTC))

Last edited at 21:58, 14 May 2007 (UTC). Substituted at 16:01, 1 May 2016 (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

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

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

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)

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)

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)

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?

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
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:

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: ${1 \over \sin A}=\csc A$ ...(or)... ${1 \over \csc A}=\sin A$ ${1 \over \tan A}=\cot A$ ...(or)... ${1 \over \cot A}=\tan A$ ${1 \over \sec A}=\cos A$ ...(or)... ${1 \over \cos A}=\sec A$ Reading down any triangle gives the Standard identities (starting at the top and going clockwise): $\sin ^{2}A+\cos ^{2}A=1\$ $1+\cot ^{2}A=\csc ^{2}A\$ $\tan ^{2}A+1=\sec ^{2}A\$ Reading a function and dividing the two consecutive clockwise or counter clockwise neighbors gives these identities: (Starting at Tan and going clockwise) $\tan A={\sin A \over \cos A}$ $\sin A={\cos A \over \cot A}$ $\cos A={\cot A \over \csc A}$ $\cot A={\csc A \over \sec A}$ $\csc A={\sec A \over \tan A}$ $\sec A={\tan A \over \sin A}$ (Starting at Tan and going counter-clockwise) $\tan A={\sec A \over \csc A}$ $\sec A={\csc A \over \cot A}$ $\csc A={\cot A \over \cos A}$ $\cot A={\cos A \over \sin A}$ $\cos A={\sin A \over \tan A}$ $\sin A={\tan A \over \sec A}$ Reading a function and multiplying the two nearest neighbors gives these identities (starting at Tan and going clockwise): $\tan A={\sin A*\sec A}\$ $\sin A={\cos A*\tan A}\$ $\cos A={\sin A*\cot A}\$ $\cot A={\cos A*\csc A}\$ $\csc A={\cot A*\sec A}\$ $\sec A={\csc A*\tan A}\$ cwm9

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)

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)

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)

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

@Materialscientist and DVdm: OOPS, the edit here of 117.198.245.180 (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

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

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

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

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

relationships involving lengths and angles of triangles

to

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. 208.50.124.65 (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 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${\frac {\pi }{2}}$ . I don't see these examples listed in any article concerning trigonometric functions.

a)$f(x)={\frac {1}{x}}+{\frac {x-1}{x}}=1$

b)$f(x)=\sin ^{-1}{\sqrt {\frac {1}{x}}}+\cos ^{-1}{\sqrt {\frac {x-1}{x}}}=?$

c)$f^{1}(x)={\frac {1}{x}}+{\frac {x-1}{x}}=1$

d)$f^{2}(x)=\sin ^{-1}{\sqrt {\frac {1}{x}}}+\sin ^{-1}{\sqrt {\frac {x-1}{x}}}=90$

e)$f^{3}(x)=\cos ^{-1}{\sqrt {\frac {1}{x}}}+\cos ^{-1}{\sqrt {\frac {x-1}{x}}}=90$

f)${\sqrt {\frac {x-1}{x}}}$

where ${\sqrt {(}}x-1)$is a slope and included in$\tan ^{-1}{\sqrt {(}}x-1)$

199.7.157.45 (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

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:

• acoustic phonetics is concerned with acoustics of speech: The spectro-temporal properties of the sound waves produced by speech, such as their frequency, amplitude, and harmonic structure.

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 (talk • contribs) 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)

File:Marcelius Martiroianas 5- u moksliu atradejas tame tarpe kurybai BIOMECHANICS et LOGICS 2oo3m

Triangle identities

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

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 ([3]) and moved the canadarm to article Uses of trigonometry ([4]). - DVdm (talk) 08:22, 19 August 2015 (UTC)

List of specific values

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

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 193.219.130.163 (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

193.219.130.163 (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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Possible Update to History Section

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: http://www.sciencedirect.com/science/article/pii/S0315086017300691

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

I seriously doubt that Ptolemy printed trigonometric tables. If he did, the Wiki article on the history of printing will need revision!109.149.91.204 (talk) 18:48, 8 February 2018 (UTC)

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

Semi-protected edit request on 26 August 2017

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.

Souces: http://www.bbc.co.uk/programmes/p05d7qps http://www.independent.co.uk/news/science/babylonians-trigonometry-develop-more-advanced-modern-mathematics-3700-years-ago-ancient-a7910936.html https://arstechnica.com/science/2017/08/ancient-tablet-reveals-babylonians-discovered-trigonometry/

many thanks 86.183.125.31 (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 201.124.223.123 (talk) 21:36, 27 August 2018 (UTC)

$\sin A$ where $A$ is a vertex in the diagram not an angle

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 $\alpha ,\beta .\gamma$ or $\theta ,$, where the Greek letters denote some angle. — Preceding unsigned comment added by 201.124.223.123 (talk) 21:59, 27 August 2018 (UTC)

Merge proposal

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 (talk • contribs) 00:42, 28 August 2018 (UTC)

Semi-protected edit request on 25 February 2019

Section Law of sines -> First formula a/sinA ... sinC is written as sirC. Change this to sinC 31.209.60.112 (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.

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.

"Proposed"

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 (talk • contribs) 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:

"Current"

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, [5], [6], [7]. 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 (talk • contribs) 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:

• [8]: "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".
• [9]: "... the length AN = cos A. This is the projection of P onto the x-axis"
• [10]: see figure 3-8: "... A_x = A cos θ"
• [11]: see figure 2
• [12]: see figures 3-8, 3-9
• [13]: see figure 6-27
• [14]: 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)

Where are the Indian mathematicians?

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)

"which are equations used for rewriting trigonometrical expressions to solve equations"

weird wording--Reciprocist (talk) 15:06, 5 January 2021 (UTC)

 Unweirded: [15]. - DVdm (talk) 17:15, 5 January 2021 (UTC)

It is still weird, identities are not equations, and what is "equations used to solve equations"?--Reciprocist (talk) 18:31, 10 January 2021 (UTC)

As far as I can see, identities, being equalities, are equations indeed. And equations used to solve other equations, is like words used to explain other words, or sentences used to explain other sentences. I see no problem with the current wording, and don't see anything weird about it. - DVdm (talk) 19:12, 10 January 2021 (UTC)

 Fixed: 3 = 2 is a (wrong) equality that is not an identity, nor an equation. So, as this article is aimed for beginners in mathematics, these technical terms must not be used in a way that is ambiguous, although correct. Thus this sentence needed to be rewritten with the use of unambiguous terms and links for them. By the way, it is a pity that "equation" is used in English for both a true equality and an equality that is to be solved. Unfortunately I cannot change that, but a careful choice of wording allows avoiding confusion. D.Lazard (talk) 19:37, 10 January 2021 (UTC)

Almost funny, this. Thanks - DVdm (talk) 00:06, 11 January 2021 (UTC)

Broken link

The External link to the book by Michael Corral is broken :

 http://www.mecmath.net/trig/trigbook.pdf

I have located a possible replacement :

 https://web.archive.org/web/20201216180745/http://mecmath.net/trig/trigbook.pdf

Can someone verify and correct this error?

Thank you. — Preceding unsigned comment added by 2600:1010:B014:9FB4:C36E:79D6:745B:DE08 (talk) 03:39, 9 March 2021 (UTC)

This page is protected from editing by unauthorized persons. The above suggestion to correct a broken link has not yet been approved or rejected. The book itself, by Michael Corral is quite a good reference. Can someone with the appropriate authority please correct this broken line.

Thank you. — Preceding unsigned comment added by 2600:1010:b002:804c:7f7b:2670:b508:d28b (talk • contribs)

 Done Thank you for the correction! - MrOllie (talk) 22:10, 30 July 2021 (UTC)

Do not lock it

Why have you locked this article coz I really need it right now 41.116.110.167 (talk) 12:38, 28 November 2021 (UTC)

Because of "Persistent vandalism: constant vandalism magnet". Have a look at the protection history. - DVdm (talk) 13:01, 28 November 2021 (UTC)

Wiki Education Foundation-supported course assignment

This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Reichara23. Peer reviewers: Reichara23.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 11:44, 17 January 2022 (UTC)

Semi-protected edit request on 19 January 2022

Please add electrical to the list of applications for trig. 2605:8D80:32E:E8C2:40A7:2786:82B4:7234 (talk) 14:13, 19 January 2022 (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 and provide a reliable source if appropriate. Cannolis (talk) 15:38, 19 January 2022 (UTC)

Mayans etc

What did the Mayans and the Aztecs know about trigonometry? Peter Horn User talk 17:03, 13 April 2022 (UTC)

Pronunciation of SOH-CAH-TOA

The current IPA given for SOH-CAH-TOA is /soʊkæˈtoʊə/. I believe that is mistaken. As per Help:IPA/English, /æ/ is the vowel in the word "trap" or "cat". For starters, the short vowel /æ/ rarely appears in an open syllable in English. Earlier revisions of this page had /soʊkəˈtoʊə/, with a schwa /ə/ for the CAH vowel, which I believe is more correct.

Currently the pronunciation is uncited. The earlier revisions cited Mathworld, which doesn't specify pronunciation. The pronunciation I am familiar with is similar to Krakatoa, and other sources online corroborate that, although none seem definitive. There could be differences between regional varieties of English.

@Nishānt Omm: when you made your edit at Mnemonics in trigonometry, were you just making that page consistent with this one, or do you in fact pronounce "CAH" using the vowel /æ/? Apocheir (talk) 18:43, 20 April 2022 (UTC)

I'm not a native English speaker. I was just making that page consistent with the main article of trig. According to wikitionary, the IPA transcript of Sohcahtoa has the vowel /ɑ/or/ʌ/ instead of /æ/ In my opinion, You should give proper references to a dictionary to defend your attitude. Nishānt Omm (talk) 02:54, 21 April 2022 (UTC)

Semi-protected edit request on 18 July 2022

KeepSanatan (talk) 13:34, 18 July 2022 (UTC)

Want to add some more substantive information about it.

Please let me make edit in semi protected pages KeepSanatan (talk) 13:35, 18 July 2022 (UTC)

the father of trigonometry is Aryabhata I, also known as the father of zero. He is an Indian mathematician and astronomer. Aryabhata gathered and elaborated the improvements of the Siddhantas points in path-breaking literature, the “Aryabhatiya”. KeepSanatan (talk) 13:36, 18 July 2022 (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 and provide a reliable source if appropriate. WelpThatWorked (talk) 15:16, 18 July 2022 (UTC)

How would one

How would one calculate the area of a piece of land, or lot, of 4 unequal sides without being given the angles? Peter Horn User talk 17:30, 13 April 2022 (UTC)

Sorry, this is not a mathematics forum. - S L A Y T H E - (talk) 06:37, 15 March 2023 (UTC)

Why should Wikipedia care?

Because the article should be accessible to high school students, and because when these students ask questions on math.stackexchange about the possibility of trigonometric proof of the Pythagorean theorem, they get incorrect answers that the trigonometric functions are defined by Taylor series, hence the proofs of the Pythagorean theorem are circular. Also, the "professional mathematicians" at math.stackexchange immediately troll and down vote correct answers, which point to their erroneous claim.

In summary, mentioning that the two definitions are equivalent only for flat space is NOT a pedantic insertion by me so that @user:jacobolus can delete it as "unhelpfully pedantic. in spherical/hyperbolic trigonometry no one ever takes ratios of angle-measure- or intrinsic-length-valued sides".

Keep in mind that Wikipedia is NOT intended solely for reading by persons who already have PhD in mathematics. The general reader would like to know that the trigonometric ratio definition does not work for curved space. After all, remember, he is general reader and does not know what mathematicians do or do not do, until the article says so.

In summary, what I expect? I expect that @user:jacobolus self-reverts his revert of my edit. Danko Georgiev (talk) 11:09, 8 April 2023 (UTC)

Your edit gives a misleading impression of the history/practice of trigonometry, which is at best going to go unhelpfully over the heads of the readers you are worried about, if it doesn’t confuse them. There is no such thing as “trigonometric definitions of sine and cosine” in curved space, the way your additions to Pythagorean theorem imply. Spherical trigonometry has a wide variety of formulas, none of which involve directly dividing the sides (for a triangle ABC on a sphere with center O, the "sides" are the measures of the central angles a = ∠BOC, etc.).

incorrect answers that the trigonometric functions are defined by Taylor series – this is a matter of convention (in this case, the convention followed by most modern advanced mathematics books). The traditional definition (from ~200 BC until ~1700) of the sine, cosine, tangent, secant, etc. was particular line segments associated with a circular arc. These originally arose in the context of spherical trigonometry (part of astronomy), no flat triangles in sight. –jacobolus (t) 14:46, 8 April 2023 (UTC)

Your reply is deeply confused, as evident from "There is no such thing as “trigonometric definitions of sine and cosine” in curved space". You seem not to be able to comprehend that a Definition contains ALL THE INFORMATION IN ITSELF. You do not have to mention any history in order to discuss the following

Definition: "sine is the ratio of opposite side to hypotenuse in right triangle".

The definition does not say whether the right triangle is drawn "inside flat space" or "inside curved space". It is exactly because the definition is silent on the curvature of the space that it is not equivalent to the analytic Taylor series. If the definition DOES NOT SAY ANYTHING about the curvature, you can apply the given definition either in flat space or in curved space. In fact, if you do not specify that you are drawing the "right triangle" inside a flat space, all of the formulas given as relation to the analytic functions will be FALSE. Danko Georgiev (talk) 15:22, 8 April 2023 (UTC)

This definition is never used outside the context of plane geometry (in particular, introductory high-school-level textbooks of the past century or two?), and implying that it is is misleadingly ahistorical. –jacobolus (t) 15:51, 8 April 2023 (UTC)

If you do not say what the context is, e.g. you wrote "the context is plane geometry", everything written in the article will be false. You cannot assume that a reader who does not know what is "the context" will guess what you could have written explicitly but did not write because you expected the reader to telepathically know. By the way, when you say "the context is plane geometry", I have no idea why you changed the word "flat geometry" to "plane geometry". "Plane" by definition is a two-dimensional surface. Are you talking about "flat plane" or about a "curved plane"? Do you by chance want to say that "the context is FLAT plane geometry"? Danko Georgiev (talk) 16:01, 8 April 2023 (UTC)

You seem to have non-standard foundational conceptual understanding and non-standard definitions of basic terms. That’s fine – for yourself – but before imposing those on heavily viewed Wikipedia articles, you must find corroborating reliable sources and consider WP:UNDUE and WP:FRINGE. Wikipedia is intended to reflect the consensus of mainstream published works, and is not the best venue for exploring alternative definitions unless they are supported by published sources. Edit: to elaborate, the “plane” in “plane geometry” or “planimetry” refers to the so-called Euclidean plane; the Latin “planum” and the French “plan” from which the English term arises literally mean “flat surface”. Both this and the English word “flat” ultimately descend from the same Greek root, πλατύς. ––jacobolus (t) 16:17, 8 April 2023 (UTC)

Did people take into consideration Euclid's 5th parallel postulate when they invented the word "plane"? Doing linguistic analysis on the origin of a word is NOT a valid mathematical method of proving theorems. Danko Georgiev (talk) 17:04, 8 April 2023 (UTC)

When mathematicians or scientists use the unqualified word “plane” (both historically and today) they almsot always mean the Euclidean plane, except in contexts where some other kind of plane is obviously more relevant. –jacobolus (t) 18:04, 8 April 2023 (UTC)

If you want an analogous spherical-geometry definition of the sine of an angle (dihedral angle) in a right-angled triangle, you need to take the ratio of the sine of the opposite side (central angle) to the sine of the hypotenuse. ––jacobolus (t) 15:55, 8 April 2023 (UTC)

You are changing the subject. I do not want analogous spherical-geometry definition. Instead, I am using exactly the definition as it is written in the main text. The main text does not introduce that the context is "plane geometry". In fact, I am using the term "flat space" because the issue is the "flatness". Is the space "flat" or is it "curved"? When you say "the context is plane geometry", I have no idea why you changed the word "flat geometry" to "plane geometry". "Plane" by definition is a two-dimensional surface. Are you talking about "flat plane" or about a "curved plane"? Do you by chance want to say that "the context is FLAT plane geometry"? Danko Georgiev (talk) 16:07, 8 April 2023 (UTC)

An unqualified “triangle” in the context of this article (and every other ordinary context in mathematics, unless otherwise specified) means a triangle in Euclidean space (sometimes an unqualified “triangle” might be taken to be in affine or projective space, but in those contexts there is no concept of length or angle measure, so they don’t involve trigonometry in the sense of this article). An unqualified “right triangle” is a triangle in Euclidean space with one right-angled corner. If you want to talk about spherical right triangles or hyperbolic right triangles or Lorenzian right triangles or what have you, you need to specify that or explicitly put yourself into a context where those are the obvious subject. –jacobolus (t) 16:33, 8 April 2023 (UTC)

You are confusing "a system of axioms" with the "semantics (i.e. meaning) of a particular axiom". In absolute geometry you have the first 4 postulates of Euclid, but not the Euclid's 5th parallel postulate. In absolute geometry, you can talk about lines, planes and triangles, but you do not have "flatness" as concept, which is introduced by the Euclid's 5th parallel postulate. What you are just saying, when translated in plain English is that when you say the word unqualified “triangle” it already contains as implicit meaning all 5 postulates of Euclid. So only with you, I cannot possibly talk about a definition of "sine" or a particular definition of "triangle" because you already have in "your English" that each of these words already contain as implicit meaning all 5 postulates of Euclid !!! So if you put all 5 postulates of Euclid, in each and every word of yours, I am afraid that there is nothing more to discuss with you. Indeed, I do not know how a person can ever talk with you about each of the Euclid's postulates, separately, one by one? I have done my fair effort to communicate with you, so that you understand me. However, you never tried to establish two-way communication. OK, fine. I no longer want to correct anything in this article. Have a nice day! Danko Georgiev (talk) 16:48, 8 April 2023 (UTC)

Yes that is correct, plane trigonometry as a subject of study, about which you can find thousands of books from the past several centuries (as distinct from spherical trigonometry, a separate subject about which you can also find thousands of books; sometimes the two subjects are combined as two parts of a single volume) is built on top of Euclidean planar geometry (which had Euclid's Elements as the canonical source). This is not something I am inventing: you can go read these books for yourself. (If you would like I can provide a few dozen references to some of the more popular titles from various centuries.)

If you want to make the context more explicit in this article that is fine with me. But implying that the concept of "sine" as the ratio of sides of a right-angled triangle still applies in curved space runs contrary to centuries of convention and is confusing/misleading to readers. –jacobolus (t) 17:54, 8 April 2023 (UTC)

You may find MacFarlane (1893) "On the Definitions of the Trigonometric Functions" of some interest. ––jacobolus (t) 19:40, 8 April 2023 (UTC)

I agree mostly with jacobolus' arguments. However, his revert of Danko Georgiev's edit is fully justified for another reason: "trigonometric ratios" are defined earlier in this article, and anything that suggests another definition is definitively confusing. If one would desire to emphasize that only Euclidean geometry is used in this article, this should be done much earlier. Personally, I would oppose to such a mention, because I cannot imagine a reader who does not know basic trigonometry and knows non-Euclidean geometries. D.Lazard (talk) 18:49, 8 April 2023 (UTC)