Talk:Trigonometry

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Trigonometry was a good article candidate, but did not meet the good article criteria at the time. Once the objections listed below are addressed, the article can be renominated. You may also seek a review of the decision if you feel there was a mistake. Date of review: No date specified. Please edit template call function as follows: {{FailedGA|insert date in any format here}}

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Contents 1 SAH something TOA? 2 Mnemonics 3 Initialization 4 Definition of Sine and Cosine 5 Rational Trigonometry 6 Lagadha & trigonometry 7 Links 8 Written in "Wales"? 9 Proof section 10 Reasons for not promoting as a good article 11 Rational trigonometry 12 Merge 13 Origins/History 14 Organization 15 History 16 Introduction 17 Formula for law of cosines 18 Proposed link 19 Slight inconsistency

[edit] 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

[edit] 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

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

[edit] 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

That's all covered in Trigonometric_function.

[edit] 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)

[edit] Rational Trigonometry

New Trig has been discovered. Check out his site for more info I think that this needs to be addressed.

Yeap, and check here [1]

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)

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.

[edit] 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)

[edit] 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)

[edit] 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?

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)

[edit] 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.

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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.

[edit] 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)

[edit] 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.

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

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)

[edit] 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)

[edit] 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)

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?

[edit] 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)

[edit] 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)