Talk:Inverse trigonometric functions

message: In \tan(\theta) , I understand that \theta is an angle, but for \arctan(a), what is a called? SDSpivey (talk) 06:11, 23 May 2020 (UTC)
replies: text: Generally, I've just seen it referred to as the "input", and that works regardless of the geometric interpretation of the numerical values (meaning it works for complex values as well). However, if you interpret it using the usual soh-cah-toa, you could call it the "side ratio" since it's the ratio of the opposite and adjacent sides. If you instead interpret it in the context of a triangle with adjacent side equal to 1, then it's just the opposite side of the triangle, as seen in the relationships between... section. Sorry if this response was too slow to be useful. BlackEyedGhost (talk) 04:02, 28 May 2020 (UTC)
thread_title:  Parameter 

message: Does anyone known where that awful sin-1(x) notation originated? I know it goes back a long way... I have seen in in 19th century textbooks. Tfr000 (talk) 13:28, 13 June 2012 (UTC)
replies: text: Good question. To do it justice, we'd also need to know the histories of the notation for exponentation and of the notation for inverses of arbitrary functions. Cesiumfrog (talk) 06:45, 14 June 2012 (UTC)
replies: text: Found it... and added it to the article. Tfr000 (talk) 19:35, 26 May 2015 (UTC)

text: 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. 5.173.127.102 (talk) 00:07, 11 March 2024 (UTC)
thread_title:  History of the sin<sup>-1</sup>(x) notation? 

message: see also
 :ru:Обсуждение:Тригонометрические функции#Радианы, & :ru:Обсуждение:Безразмерная величина#Единица измерения (?!?) безразмерной величины… --De Riban5 (talk) 09:03, 17 January 2015 (UTC)
replies: text: You don't need to include the category to the WP article in another language. You can click on the language on the left side. M∧Ŝc2ħεИτlk 11:28, 17 January 2015 (UTC)
thread_title:  Radian… and [[:Category:Dimensionless numbers|category]] 

message: In the "Relationships between trigonometric functions and inverse trigonometric functions" table we can see the arccsc(x) function has a white background. Any ideas on how we can fix that? It sticks out like a sore thumb.
--Jason B. (talk) 21:01, 13 April 2016 (UTC)
thread_title:  Inverse cosecant formatting 

message: Looking back at the old history of this article, it seems as if the e's, the i's, and the dx's were all typeset in their more standard italic version, in contrast to how it is now.  I'd like to put things back, but according to WP:MOSMATH, one should not go through and make these sorts of changes wholesale.  However, I think it's warranted here, as this must have been done at some point in the article's past anyway, and this change would simply put it back to its original form.  This is especially important for the i's and the e's, as roman versions are extremely nonstandard.  Any thoughts/objections?  Deacon Vorbis (talk) 21:23, 11 February 2017 (UTC)
replies: text: I'm going to go ahead and make the changes.  If anyone seriously objects, let me know here.  Deacon Vorbis (talk) 14:51, 24 February 2017 (UTC)
thread_title:  Roman vs italic 

message: Hello all! I wondered if there is any standard expression of the inverse trigonometric functions in exponential form. I believe that the standard trigonometric functions can be expressed in exponential form, and that this form is of sufficient import to sometimes be used as the definition of these functions. I was reminded of this when I saw the infinite series section, because the exponential function can be represented and defined as an infinite series.
If there exist such a representation, could it be mentioned here?
Thanks for reading! JonathanHopeThisIsUnique (talk) 05:03, 30 November 2017 (UTC)
replies: text: See Inverse trigonometric functions#Logarithmic forms. JRSpriggs (talk) 22:29, 30 November 2017 (UTC)
thread_title:  Exponential Form 

message: The change I made on 2020-09-03 was reverted on 2020-09-05. I believe it was valid. I now also have several changes to the Logarithmic Forms that I believe make them valid everywhere for principal values of the functions, not just on the complement of the branch cuts. If anyone wants to review these identities in advance of my posting them, please reply here within the next 48 hours. Rickhev1 (talk) 18:28, 8 September 2020 (UTC)
thread_title:  Complex logarithmic forms 

message: This is nicely written subsection. That's where Wikipedia shines. I think we should extend such subsections. --AXONOV (talk) ⚑ 10:00, 7 July 2021 (UTC)
thread_title:  Applications section 

message: The nice thing about the Arc- names is that they always remind you that the arc functions give back an Angle. 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. Acorrector (talk) 11:52, 22 November 2021 (UTC)
thread_title:  Arc --> Angle 

message: The 4th column in the first table of the section contains typographical errors in rows 4 and 5.
Moreover, in the 4th column of rows 3, 4, 5 it may be questioned whether k \pi is overspecified in the light of the \iff and the rows 1, 2, 6, 7, 8. Nomen4Omen (talk) 15:31, 18 September 2022 (UTC)
thread_title:  Solutions to elementary trigonometric equations (≥ 2 questions for editor 9.51.61.147)