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{{WikiProject Mathematics|importance=high}}
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== Parameter ==
In <math>\tan(\theta) </math>, I understand that <math>\theta</math> is an angle, but for <math>\arctan(a)</math>, what is <math>a</math> called? [[User:SDSpivey|SDSpivey]] ([[User talk:SDSpivey|talk]]) 06:11, 23 May 2020 (UTC)
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I disagree it is "awful". It is the notation of an inverse function after all. I also find that students get a better understanding when asked to find the derivative of y=sin<sup>-1</sup>(x), they instantly understand x=sin(y) (and then can differentiate implicitly). [[User:Jim77742|Jim77742]] ([[User talk:Jim77742|talk]]) 00:11, 20 November 2017 (UTC)
:But arcsin(y) is not an actual inverse of general sin(x), but of sin(x) on a specific interval -pi/2, pi/2. A function must be a bijection to posses an inverse. Without specifying an interval, sin(x) is not a bijection. [[Special:Contributions/5.173.127.102|5.173.127.102]] ([[User talk:5.173.127.102|talk]]) 00:07, 11 March 2024 (UTC)
== Extension to complex plane ==
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<< I copied this from my talk page. [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 08:01, 15 April 2013 (UTC) >>
Thanks a lot! That section looks better now ☺. Well, I see an issue with the notation used on Wikipedia for the inverse trigonometric functions, i.e., the convention here is to denote all functions with minuscule letters but to add the word arc with the inverse ones (sin x, arcsin x, etc...) but what we (along with our textbooks) do, is to denote regular functions with minuscule letters, e.g., sin x, cos x, etc., and the inverse functions with the first letter majuscule and a −1 superscript, e.g., Sin<sup>−1</sup> x, Cos<sup>−1</sup> x, etc., which causes no confusion between the inverse function (Sin<sup>−1</sup> x) and the multiplicative inverse (sin<sup>−1</sup> x). This notation is nowhere to be found here. I personally find the arc notation a bit odd. Do you find this (capital) notation at least worth mentioning in [http://en.wikipedia.org/wiki/Inverse_trigonometric_functions the article] (if the arc notation is popular and cannot be removed)? Hoping to get a reply in the affirmative... Regards, <div align=right>— S'''<span class="smallcaps" style="font-variant:small-caps;">yɛd</span>''' [[User:Syed_Wamiq_Ahmed_Hashmi|<
:I would rather not change the notation that way. Superscript minus one could be misinterpreted as the multiplicative inverse rather than the inverse with respect to composition. Please see the archive, [[Talk:Inverse trigonometric functions/Archive 1]], for more discussion of this issue.
:When referring to one of our articles or talk pages, please use <nowiki>[[this method]]</nowiki> rather than <nowiki>[http://en.wikipedia.org/wiki/this_method this method]</nowiki> . [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 08:01, 15 April 2013 (UTC)
:: O.K., Now, I’ve got the things you said. I’ll do them as such. As to the notation, the article [[Inverse function]], too, uses ''f''<sup>−1</sup> for the inverse function of ''f'' which here, means the compositional inverse (the −1 doesn’t mean multiplicative inverse which would be denoted by (''f'')<sup>−1</sup>...) So, are you satisfied as to the use of −1? Moreover, as I have already said, this notation doesn’t clash with that for the multiplicative ones. I have seen the archive and I do not demand replacement now, but just a bare mention (like somthing in the beginning of the article, saying that these notations are also used, which don’t cause confusion; for other people like me who don’t use and are unfamiliar with the arc notation). <div align=right>— S'''<span class="smallcaps" style="font-variant:small-caps;">yɛd</span>''' [[User:Syed_Wamiq_Ahmed_Hashmi|<
ISO80000-2-13 states "(sinx)<sup>n</sup>, (cosx)<sup>n</sup>, etc., are often written sin<sup>n</sup>x, cos<sup>n</sup>x, etc." But there is no mention of sin<sup>−1</sup>x for arcsinx. <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/83.223.9.100|83.223.9.100]] ([[User talk:83.223.9.100#top|talk]]) 10:46, 12 January 2017 (UTC)</small> <!--Autosigned by SineBot-->
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So wait, this is still left ambiguous. Have we all collectively decided to uphold the standards from that book? Or should we uphold the standards from the NIST website? [[User:Math Machine 4|Math Machine 4]] ([[User talk:Math Machine 4|talk]]) 19:35, 15 December 2020 (UTC)
Furthermore, could someone who owns that book please verify if that claim is accurate? Because, I'm pretty doubtful that they'd change the international standard for something and only announce that new standard in one single book, but fail to update their websites to account for said update. [[User:Math Machine 4|Math Machine 4]] ([[User talk:Math Machine 4|talk]]) 23:42, 19 December 2020 (UTC)
Actually, come to think of it, since that book came out in 1964 (before the Internet), and the current standard displayed on the NIST website is different, wouldn't that mean that the definition given in that book is outdated? Unless the NIST stopped being the international standard some time between 1966 and whenever they got a website, how is this even up for debate? [[User:Math Machine 4|Math Machine 4]] ([[User talk:Math Machine 4|talk]]) 23:54, 19 December 2020 (UTC)
NIST is not an international standard; it's a national standard (hence the N). The ISO (which is international, hence the I) uses 0 < <i>θ</i> < π, or at least it did in 2009. See page 25 of the PDF at https://people.engr.ncsu.edu/jwilson/files/mathsigns.pdf (this is a scan of the 2009 standard, since you have to pay over $100 for the current standard, but I don't believe that it has changed). This is also in several American trigonometry textbooks that I've used, so I can cite them if you want American sources (to go with NIST and Wolfram, which are also American). [[User:Toby Bartels|Toby Bartels]] ([[User talk:Toby Bartels|talk]]) 01:50, 11 March 2021 (UTC)
:So, we're just going to let this whole Wikipedia article contradict itself, constantly swapping between one definition and the other, just because no internet user on the entire Earth is willing to pay $160 to see what the current international standard is? So we'll just say "do them both?". Why would this even cost money, shouldn't an international standard be in the public ___domain? If they're so important, why don't they get funding from somewhere else? Or better yet, instead of charging a week worth of rent for a silly article (it depresses me to know that that's only a week), why not charge something reasonable, like $20? I'd pay $20 to read that article. You have to realize, there are 12 parts. If someone tried to pay for all 12 parts, that'd be $1200 and 2 of the parts would be missing.
:In any case, let's give the benefit of the doubt and say the standard hasn't changed. Because it probably hasn't. There still isn't anything on the inverse trig functions for complex numbers, which I find completely ridiculous. We either say we can't take inverse trig functions of complex numbers (which is a blatant lie), or that the NIST is the standard for complex numbers, while the ISO is the standard for real numbers. Which doesn't make any sense because real numbers are to complex numbers what thumbs are to fingers. And also, I see NO REASON WHATSOEVER for NIST and ISO to have different standards. It completely DEFEATS THE PURPOSE of a standard: for things to be unambiguous. One answer. That's what upsets me. That and the fact it was even considered okay to cite a book nobody has access to as a source, but that's pretty much irrelevant at this point.
:Let's just be honest on the article: "In order to take an arc cotangent, first, ask yourself: are you in America, or somewhere else in the world? If you answered America, you first take the reciprocal, then take the arctangent. If you're in some other country, take the arctangent, and subtract it from π/2." Yeah, it sounds silly, doesn't it? Well, too bad it's true. And again, too bad they didn't define it for complex numbers. You could say "Well, obviously, for complex numbers, you just do the same thing." Except no. The definition they list implies both the input and output are real numbers. They said nothing about subtracting anything from π/2, all they said was "the answer to cot(y)=x over the interval (0,π)" (paraphrased). I don't even know who I'm arguing with at this point, I'm just ticked off at how stupid this is.
:And also, if anyone wants to pay $160 to see that article, here ya go: https://www.iso.org/standard/64973.html. PS, it only takes Swiss Francs, for some reason. Not even Euros, but Francs. If you're a gambling man, and want it at a discount, here ya go: https://www.docuarea.org/home/19852-ISO-80000-2-2019.html, but I cannot guarantee it's not a scam, nor can I guarantee it's being legally hosted. All I can say is it exists. And P.P.S., if someone does buy it, and they're legally allowed to, could they please host a picture of the arccotangent part on imgur and post the link here? Thanks. [[User:Math Machine 4|Math Machine 4]] ([[User talk:Math Machine 4|talk]]) 23:28, 12 June 2022 (UTC)
== Radian… and [[:Category:Dimensionless numbers|category]] ==
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:I'm going to go ahead and make the changes. If anyone seriously objects, let me know here. [[User:Deacon Vorbis|Deacon Vorbis]] ([[User talk:Deacon Vorbis|talk]]) 14:51, 24 February 2017 (UTC)
There's no need to change the article now, but upright d<i>x</i>, e, and i are all standard according to the ISO. See pages 22&23, 24, and 27 (respectively) of the PDF file at https://people.engr.ncsu.edu/jwilson/files/mathsigns.pdf (this is a scan of the 2009 standard, since you have to pay over $100 for the current standard, but I don't believe that it has changed). [[User:Toby Bartels|Toby Bartels]] ([[User talk:Toby Bartels|talk]]) 01:53, 11 March 2021 (UTC)
== Exponential Form ==
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:: Hi Deacon Vorbis,
:: Thank you for your feedback! It is very inconvenient to find a particular information about a function when everything is merged together. As I have mentioned, it is OK to keep everything merged. I am not against it. However, there should be independent pages as well for each trigonometric functions. Many popular handbooks in math keep each trig functions in a separate chapter to make convenient to find more specific information without wasting time of a reader. This is a common convention and '''we should follow this convention'''. Therefore, there should be more options for the readers. Some readers prefer to read merged version while other readers would be more comfortable for trig functions written in individual pages. Let's make this option for readers. They will decide themselves according to their needs and convenience. For me, reading this merged version is very inconvenient due to extra information that takes lot of my time. I would prefer [[MathWorld]] format that adopts individual pages for each function. I am sure there are plenty of people who would prefer individual pages as well. We should be more democratic '''to allow readers to have a choice between merged and unmerged versions''' that they find more convenient for their needs rather than to impose the only merged format to everyone. Let's both versions be present! It will be very reasonable to give this choice to the Wikipedia readers. [[User:Math&App|Math&App]] ([[User talk:Math&App|talk]]) 00:52, 7 October 2020 (UTC)
== Applications section ==
This is nicely written subsection. That's where Wikipedia shines. I think we should extend such subsections. --<span style="font-size: small" >[[User:Alexander_Davronov|<span style='color:#a8a8a8'>AXO</span><span style="color:#000">NOV</span>]] [[User talk:Alexander_Davronov|(talk)]] [[Special:Contributions/Alexander_Davronov|⚑]]</span> 10:00, 7 July 2021 (UTC)
== Arc --> Angle ==
The nice thing about the '''A'''rc- names is that they always remind you that the arc functions give back an '''A'''ngle. Look at some complicated formula involving arctans and arcsines and at least you know the 'arcs' are giving you nothing more complicated than an angle. [[User:Acorrector|Acorrector]] ([[User talk:Acorrector|talk]]) 11:52, 22 November 2021 (UTC)
== Solutions to elementary trigonometric equations (≥ 2 questions for editor 9.51.61.147) ==
The 4th column in the first table of the section contains typographical errors in rows 4 and 5.<br />
Moreover, in the 4th column of rows 3, 4, 5 it may be questioned whether <math>k \pi</math> is overspecified in the light of the <math>\iff</math> and the rows 1, 2, 6, 7, 8. [[User:Nomen4Omen|Nomen4Omen]] ([[User talk:Nomen4Omen|talk]]) 15:31, 18 September 2022 (UTC)
== India Education Program course assignment ==
[[File:Wikipedia-Ambassador-Program-Logo.png|50px]] This article was the subject of an educational assignment supported by [[Wikipedia:Education program/Ambassadors|Wikipedia Ambassadors]] through the [[Wikipedia:India Education Program|India Education Program]].[[Category:India Education Program student projects|{{PAGENAME}}]] [[Category:India Education Program student projects]]
{{small|The above message was substituted from {{tlc|IEP assignment}} by [[User:PrimeBOT|PrimeBOT]] ([[User talk:PrimeBOT|talk]]) on 20:02, 1 February 2023 (UTC)}}
== Anybody in here? ==
All I see (without using the inspector tools) if I look at e. g. Basic concepts / Principal values is (cut down to its roots):
<hr>
<table>
<tr>
<th>Name</th>
<th>Usual notation</th>
<th>Definition</th>
<th>Domain of for real result</th>
<th>Range of usual principal value <br> (radians)</th>
<th>Range of usual principal value <br> (degrees)</th>
</tr>
<tr>
<td><b>arcsine</b></td>
<td></td>
<td><i>x</i> = sin(<i>y</i>)</td>
<td></td><td></td><td></td>
</tr>
<tr>
<td><b>arccosine</b></td>
<td></td>
<td><i>x</i> = cos(<i>y</i>)</td>
<td></td><td></td><td></td>
</tr>
<tr>
<td><b>arctangent</b></td>
<td></td>
<td><i>x</i> = cot(<i>y</i>)</td>
<td></td><td></td><td></td>
</tr>
<tr>
<td><b>arccotangent</b></td>
<td></td>
<td><i>x</i> = cot(<i>y</i>)</td>
<td></td><td></td><td></td>
</tr>
<tr>
<td><b>arcsecant</b></td>
<td></td>
<td><i>x</i> = sec(<i>y</i>)</td>
<td></td><td></td><td></td>
</tr>
<tr>
<td><b>arccosecant</b></td>
<td></td>
<td><i>x</i> = csc(<i>y</i>)</td>
<td></td><td></td><td></td>
</tr>
</table>
<hr>
Maybe you’re overscripted? <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/93.229.109.29|93.229.109.29]] ([[User talk:93.229.109.29#top|talk]]) 04:46, 28 September 2024 (UTC)</small> <!--Autosigned by SineBot-->
:Something is going wrong on your end. These all render using Wikipedia's backend LaTeX->SVG tool, and should appear as SVG images in your browser. Have you tried reloading the page, possibly after clearing caches? Does your browser have an unusual configuration? –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 06:14, 28 September 2024 (UTC)
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