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Gave
Willingly was taught to me in college, believe it or not. (Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Gray, White - I still remember it 60 years later...) Anyway, I was taught, even earlier than the resistor color code, "All Students Take Calculus" which perhaps isn't as useful today, since trig is (apparently) no longer the "gateway" into precalculus. I suggest an encyclopedia isn't an appropriate place for insults, even if the intent isn't malicious.
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mentioned in a half sentence. There is one sentence about "The sine and cosine functions are one-dimensional projections of uniform circular motion" but this should be a whole section. There is no discussion of the relation of trigonometric functions to vectors, but this should also be a whole section. There is one example of a
Fourier series, but this should again be a whole section. The section
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in this context. I think any such discussion should clearly and explicitly point out that (a) the half-tangent is itself a "trigonometric function" of angle, and (b) it's an alternative representation to angle measure, in terms of which other trigonometric functions can be described rationally, making it to a substantial extent a way to
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one has to be careful about which sheet of the covering space one is on, because a periodic function of period 2Ď is being described in terms of a periodic function of period Ď. Hardy does this by continuation using a quarter period, but that's needlessly complicated. I'll try to track down a source that explicitly uses this approach.
1620:â, begins, âIf the acute angle θ is given, then any right triangles with an angle of θ are similar to each other.â How about, âAny two right triangles with the same acute angle θ, are similar to each other.â (I include a comma after a long subject of a sentence, such as here, for legibility.) Also, could âto each otherâ be removed?
1080:. But in any event, this is awfully mild and lighthearted to be called "outrageous", given all of the actually outrageous things in the world. (By comparison, your mnemonic joking about rape is quite gratuitously crass and sexist, and perhaps racist, and any teacher presenting it today could expect to be fired.) â
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citation in the footnotes. If you add a source used for just one claim, or a source used a few times but which is short enough to not need a page specified or where the pages used are the same for all cited claims, put it directly into a footnote. Feel free to also add textual notes to the 'notes' section. â
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I'm still a bit concerned about this new section. I think it's a bit misplaced and somewhat misdirected. The half-tangent is well worth mentioning somewhere here, but the "analysis" section is not the right place in my opinion, and I think the way this one is currently written gives this undue weight
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But
Quantling makes a good point that "All Students Take Calculus" is better on other grounds. Moreover, poking into the literature, it doesn't appear that people actually favor one mnemonic over another to a great extent here, so we shouldn't imply that only one mnemonic exists. I've gone ahead and
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et al., I have heard many people talk about "SOHCAHTOA". Although I don't have a citation at hand, I think it is improvement to the article to discuss SOHCAHTOA. Hopefully, someone will come up with a citation pronto and this will all be moot but, even if not, might we keep this discussion anyway?
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with the comment "Sqrt(2)/2 is much more common than 1/sqrt(2) in the literature". Though I understand that â2/2 is more common, the line gives it twice. I wonder if it may help learners to know that both expressions are valid, should they come across the rarer form. Does anyone have any thoughts on
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The second paragraf says, âThe trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions
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I'm not married to using the tangent half-angle substitution instead of the tangent substitution. But it seems to me that the former is a lot simpler, and many of the basic properties of the trigonometric functions (especially their period) are more obvious. Actually defining them via the tangent,
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Perhaps we could replace "All
Science Teachers (are) Crazy" with "All Students Take Calculus". The latter is slightly better to me as a mnemonic because it doesn't have the extra word "are", and it has the added advantage of avoiding the potentially offensive language. Personally, my general rule
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I am astounded that
Knowledge allows the mnemonic "All Science Teachers (are) Crazy". The term "crazy" isn't acceptable, is it? Sure it's outrageousness makes it memorable, but I can think of lots of unacceptable mnemonics. Like the resistor code Bad Boys Ravished (raped) Our Young Girls But Violet
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section is a mess in my opinion: the material currently there is basic tools of trigonometry and should be moved to separate top-level sections, but we don't mention any of the applications of trigonometry (historically astronomy, navigation, surveying, architecture, gunnery, ..., or more recently
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should be moved to top level and substantially expanded. The history section mentions "Historically, trigonometric functions were often combined with logarithms in compound functions like the logarithmic sine, ...", but this topic should again be a whole section (and ideally link to a main article
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Different countries and different authors had/have different conventions about this. In modern
English language sources "tan" is the most common, partly because it is the only one supported by default in LaTeX. But if you look at work from France, Germany, or Russia, especially historical sources,
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These were merged (a long time ago) because it was thought that most relevant material about any of them would be applicable to all of the others, many relevant features would be useful to compare from one to another, and important context was needed in common between them. People thought separate
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You are editing the style of the article (if you do this for consistency purposes, your choice has to be discussed here at the Talk page, it doesn't matter if "the code looks prettier"). Another thing I should discourage you from doing is changing "trigonometric" to "trig"; you can't do that; the
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have separate articles). Having these lumped together has discouraged people from adding useful information which applies to only one or another. Any subject which has enough to say about it independently to flesh out a self-contained article should generally have one, and there is quite a lot to
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I agree the analysis section should be later in the article. Hardy explicitly defines the trigonometric functions by integration, although he uses the tangent substitution which is algebraic rather than rational. Bourbaki defines the trigonometric functions using unitary representations of the
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There are a variety of reference styles used in
Knowledge articles, and this is one of the more common ones. If you add a source which will be used repeatedly, especially a long source with separate page numbers for the different claims, put it into 'references' and then cite it with a shortened
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is too long and is distracting at this length near the top. The historical definition used for 2000 years between the 2nd century BC and at least the end of the 18th century, of "trigonometric lines" representing line segments with respect to a circular arc, is not discussed at all and is only
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I edited the section "Radians versus degrees", lightly, for concision. "the images to the right there are not great and could probably be usefully moved or replaced, and the table's content also doesn't match the section, and it should be moved or modified." How should said images be moved or
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Could âin modern mathematicsâ be changed to âtodayâ? After all, these functions are by definition part of math, so the word âmathematicsâ is redundant. When it says â⌠cotangent functionsâ, could âfunctionsâ be removed, as it is obvious that these are functions? (More generally, can the word
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I don't understand what you mean. What kind of note are you trying to add? Feel free to mix textual notes in with the reference footnotes. If you get consensus here, e.g. if you plan to do a substantial rewrite of the article, you can probably do some amount of reformatting of the appendices.
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I don't think it's undue weight to include several definitions of the trigonometric functions that have been used in analysis. I used Hardy, in particular, because he addresses the unsatisfactory nature of the usual definition in elementary calculus, and someone had complained about it.
1709:â the images to the right there are not great and could probably be usefully moved or replaced, and the table's content also doesn't match the section, and it should be moved or modified. Shortening the captions doesn't really make a significant improvement in my opinion. â
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In the expression âTrigonometric function sin θâ, i think âTrigonometric functionâ is redundant (kind of like âin colorâ in âred in colorâ); anyone who knows what sine is, knows that it is a trig function. Also, in âsine function versus angleâ, âfunctionâ is redundant.
1252:, which grew far beyond reasonable article scope and should probably be published somewhere external to Knowledge. It will take a lot of work, especially trimming, to salvage some parts as a Knowledge article at this point, and I got quite stalled on the project.)
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you will commonly find "tang" and "tg" as an alternative. The current text in the article is fine, but if someone can find a clear discussion of this it would also be fine to more explicitly describe the relative popularity and extent of these various symbols. â
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The next sentence is, âThus these six ratios define six functions of θ, which are the trigonometric functions.â This is a bit wordy, since the word âfunctionâ is repeated. How about âThus these six ratios define the six trigonometric functions of
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But in any case, if we're going to add a section about this, its details should be well sourced and its content should be broadly reflective of the way the topic is addressed in high-level sources about trigonometric functions or trigonometry.
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Also, in said section, there is a long gap between the table, âSummary of relationships between trigonometric functionsâ, and the text above it; due to the pictures and their captions. This makes me want to shorten the captions. One caption
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Interesting. I didnât realise multiple mnemonics had been created. The one I learned as a 16-year old was âAll
Stations To Claremontâ where Claremont was a well-known station on the railway line that served the largest city in the vicinity.
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What parts of the article should be rewritten, and how? Also, what do you mean by ârandom wordsâ? Also, in the expression âTrigonometric function sin θâ, would you agree that âTrigonometric functionâ is redundant, at least in said caption?
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which would discuss the topic in detail, since no
Knowledge article currently does). There should be a whole section about the relation between circular and hyperbolic functions, but currently the latter are barely mentioned here. The
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In the article, there are references in the notes section and another section of references in the references section. This error (if it is an error) makes it impossible to annotate the article. Please someone fix this bug
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Personally, I think "All
Science Teachers (are) Crazy" is pretty tame as far as old mnemonics go; even if "crazy" is one of those stigmatizing words we should be making an effort to say less often, it's not what I'd call
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1584:"In modern mathematics" and "today" are not necessarily equivalent. "Modern mathematics" is quite old, actually. And yes, I agree with the removal of the word "function" when it appears later in the article.
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Anyway as for your specific questions: The sentences about similar triangles should be more substantially rewritten for clarity. I don't think your proposed changes are much better than what was there.
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I was on this page and I became curious: why do tangent, cotangent, secant and cosecant all share a page while sine and cosine get their own? Why can't we move them all into one page?
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This is my read, and parts of "Definitions in analysis" could be reorganized into that section, like Euler's formula, with Bourbaki's definition left in the analysis section.
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The next sentence is, âThis means that the ratio of any two side lengths depends only on θ.â Could âThis means thatâ, be replaced with âThereforeâ or âThusâ or âThat is,â?
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You mean, âIn the complex planeâ should be a first-order section, not a subsection, and should should be the first thing in the article, other than the intro?
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Several parts of this article might benefit from a substantial rewrite, but trying to cut out random words from its sentences doesn't seem that helpful. â
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I am editing this article heavily for concision, including making the wikicode more concise. I strongly feel that concise wikicode looks prettier. Okay?
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It seems to me that the approach we are crediting to Bartle and Sherbert is very likely due to Landau. It would be nice to include a reference if so.
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The development you are presenting is not Hardy's though, but your own, for which you don't have any source. At best this is "original synthesis".
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is to say what needs to be said even if it is offensive, but if you can say what you need to say without being offensive then please do! â
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Knowledge does not insult by saying that all science teachers are crazy. It reports (with a reliable source) that some people use that
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No, the complex plane section should be moved to the top level of the article, not made a subsection of "definitions in analysis". â
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separately say about sine, tangent, secant, etc., especially discussion about history. I eventually intend to make separate
1371:(though this is a self-published arXiv pdf, which probably doesn't count as a "reliable source" by Knowledge standards). â
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tg and ctg, arctg and arcctg should not be used in accordance with ISO IEC 80000-2:2009. That is absent at the article.
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Feel free to add textual notes to the numbered footnotes currently in the article. You can add these with
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No, it should clearly not be the first thing in the article. It belongs in the second half of the page. â
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Landau, Edmund (1934). EinfĂźhrung in die Differentialrechnung und Integralrechnung (in German). Noordoff.
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In retrospect I think this was the wrong decision (or rather, I think we should have an article called
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torus, as I also recently added. These seem like reasonable high-level sources for the article.
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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and the duplication probably came from the "easy way to remember" values. Probably best to omit.
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I admit, however, that i hav a habit of being aggressiv about editing articles for concision.
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Bottom: Graph of sine function versus angle. Angles from the top panel are identified.â
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It's not bad as exposition, but it should probably be published at some other venue. â
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has a corresponding inverse function, and an analog among the hyperbolic functions.â
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I think the section as currently stands violates the spirit of both
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trigonometric functions and calculus/analysis, in favor of algebra.
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went through something like four editions; which one was used here?
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Robinson, Paul L. (2019). "A tangential approach to trigonometry".
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articles would consist of substantially duplicated material.
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The text does not imply that. It says this was used as a
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replaced? How should the table be modified or replaced?
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are too long and belabor the details. The section about
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It might make sense to add a note to show it either way
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wasn't known until 1840? That seems impossible to me. â
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298:Top-priority
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1800:Tito Omburo
1598:Thank you.
1512:Tito Omburo
1392:Tito Omburo
1337:Tito Omburo
1307:Tito Omburo
1272:Tito Omburo
1238:Tito Omburo
1211:Tito Omburo
1184:OK, added.
1172:Tito Omburo
1095:outrageous.
952:Voproshatel
318:This was a
273:Mathematics
264:mathematics
213:Mathematics
1847:Categories
1508:definition
1362:1902.03140
1186:XOR'easter
1157:XOR'easter
1104:XOR'easter
1816:jacobolus
1772:jacobolus
1711:jacobolus
1657:jacobolus
1528:Concision
1496:jacobolus
1373:jacobolus
1324:jacobolus
1294:jacobolus
1258:jacobolus
1082:jacobolus
982:jacobolus
874:jacobolus
843:jacobolus
816:jacobolus
781:jacobolus
723:jacobolus
719:SOHCAHTOA
680:SOHCAHTOA
627:like this
182:is rated
1068:contribs
1060:uantling
935:1234qwer
932:1234qwer
704:contribs
696:uantling
686:D.Lazard
631:Johnuniq
395:365 days
353:Archives
103:Promoted
1121:Dolphin
992:Oh, ok
855:Bera678
828:Bera678
800:Bera678
662:Bera678
619:Crissov
601:Cheers,
322:on the
300:on the
184:B-class
141:Demoted
81:Process
1149:Bartle
605:cmɢĘee
598:this?
190:scale.
84:Result
1631:says,
1357:arXiv
1243:avoid
741:Snipe
171:This
40:is a
1804:talk
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1627:θ.â?
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1076:See
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1040:DVdm
1038:. -
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804:talk
771:and
764:also
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666:talk
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648:DVdm
646:. -
635:talk
610:ĎaĘÎş
417:DVdm
122:Kept
78:Date
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539:sin
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292:Top
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