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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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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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