3213:(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.
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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.
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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.
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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 x, Cos x, etc., which causes no confusion between the inverse function (Sin x) and the multiplicative inverse (sin 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
1161:
article mentions the complex extensions in several places, but never defines them. The article was apparently written with only the real versions in mind and then later patched to include pieces of information about the complex extensions. I think that this calls for a redesign of the whole article to give at least equal treatment to the complex extensions. And as Wamiq noticed, we need to indicate where the cuts in the complex domain are located.
185:
2135:)...) 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).
3777:. 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
3566:. This section is interesting. However, it covers everything whatever is needed and whatever is not. For me this page is OK. Let it be there. However, it looks like a textbook for inverse trigonometrical functions. It may be convenient for study of trigonometry of inverse functions, but it may be very inconvenient if one wants to find some information for a specific function like
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3193:(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).
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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.
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a bit odd, and I'd probably prefer that sine redirect to the main page with any content not already present merged in. Personally, I think the inverse functions should all be lumped together in one page as is currently done. There's always a tradeoff between splitting and merging, but here, I think
2040:
Thanks a lot! That section looks better now ☺. Well, I see an issue with the notation used on
Knowledge 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
3542:
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
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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
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NIST is a kinda of standards. What's much more important - virtually all CAS (and related mathematical software in general) agreed on that definition, both open and closed-source (i.e. Maxima, Mathematica, Maple, Matlab). I believe, this definition should be first (but we should mention others, if
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The "Expression as definite integrals" section lists expressions of the functions of x with a z^2 and dz on the right hand side, but no explanation of where this "z" comes from. It's been a while since I've had trig in school so I'm guessing I need to be reminded of what it is, and it would be good
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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
3208:
So, we're just going to let this whole
Knowledge 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
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My reference is to the "Handbook of
Mathematical Functions with Formulas, Graphs, and Mathematical Tables" by the National Bureau of Standards (which is what NIST was called before its name was changed), issued June 1964, fifth printing August 1966 with corrections. See page 79, section 4.4 Inverse
352:
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
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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
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in which he restricted the domains of the derivatives to certain subsets of the real numbers. The formulas he changed were intended to apply to extensions of the inverse functions to the complex plane (a fact which he overlooked, but is now aware of). This brings my attention to an issue — this
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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
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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.
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There are several possible ways of defining the extensions of inverse trigonometric functions to the complex plane. In addition to how the functions are computed, they may differ in where one puts the cuts between different sheets of the functions. I would like to suggest the following:
3228:, 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.
3405:, 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
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to have a small explanation at the side or bottom explaining where Z comes from. Or, if it's a typo, we need to change the expressions to have x^2 and dx rather than z. But my money is that I'm the one that needs educating. Could a section be added to clear up what "z" is?
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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(x), they instantly understand x=sin(y) (and then can differentiate implicitly).
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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!
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where all inverse functions are not merged together, but considered independently from each other. I hope you will find my suggestion reasonable. For convenience of readers this issue should be resolved in
Knowledge in future.
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the section should lead with an introductory sentence or two that also outlines how these rules are derived (with a citation to any reliable source, even a math professor's website, that performs this derivation in detail).
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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.
1800:{\displaystyle {\frac {d\arcsin z}{dz}}={\frac {1}{1+\left({\frac {z}{\sqrt {1-z^{2}}}}\right)^{2}}}\cdot {\frac {{\sqrt {1-z^{2}}}-z\left({\frac {-2z}{2{\sqrt {1-z^{2}}}}}\right)}{1-z^{2}}}={\frac {1}{\sqrt {1-z^{2}}}}\,}
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The problem I am seeing now is how do we handle the fact that there are multiple sheets in the complex domain for the inverse trigonometric functions. And they interact with the fact that the square-root has two sheets.
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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.
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2557:{\displaystyle \arccos 0.5=\int _{0.5}^{1}{\frac {1}{\sqrt {1-z^{2}}}}\,dz=\lim _{n\to \infty }\sum _{k=1}^{n}{\frac {1}{\sqrt {1-\left(0.5+(k-{\frac {1}{2}}){\frac {(1-0.5)}{n}}\right)^{2}}}}{\frac {1-0.5}{n}}}
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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
Knowledge readers.
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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,
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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
3718:. And it is very inconvenient to look for a specific information in the section that combines all inverse trigonometric functions together. Knowledge should follow the convenient style adopted by
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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
1995:{\displaystyle {\frac {d\operatorname {arcsec} z}{dz}}={\frac {-1}{\sqrt {1-z^{-2}}}}\cdot {\frac {-1}{z^{2}}}={\frac {1}{z^{2}{\sqrt {1-z^{-2}}}}}=\pm {\frac {1}{z{\sqrt {z^{2}-1}}}}\,}
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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? –
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Today I tried to open a
Knowledge page for the arctangent function. However, my suggestion was declined. According to the reviewer the page is not needed as it is already in
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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?
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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
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How about we just draw a triangle for each of the identities? Then there is no need to prove them, and the section benefits from some badly needed visual aids.
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3634:. Therefore, if some people found it sufficient, there are users who would prefer separate consideration of individual inverse function. I do not understand why
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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.
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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.
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Yesterday I just needed to plug arccot in somewhere and got quite confused. I think a caveat on this article would be nice explaining the different choice.
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I choose the former because it gives a value to arccot (0) and is continuous there whereas the latter definition is discontinuous and undefined at zero.
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3224:. 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:
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3483:(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).
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Does anyone known where that awful sin(x) notation originated? I know it goes back a long way... I have seen in in 19th century textbooks.
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NIST is not an international standard; it's a national standard (hence the N). The ISO (which is international, hence the I) uses 0 <
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Can you show evidence that there is a standard definition, agreed by virtually all authors, other than the one I gave? I do not think so.
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If we adopt that suggestion, then it may affect the signs of the derivatives of the functions. To verify what those derivatives would be:
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3401:'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
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All I see (without using the inspector tools) if I look at e. g. Basic concepts / Principal values is (cut down to its roots):
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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.
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ISO80000-2-13 states "(sinx), (cosx), etc., are often written sinx, cosx, etc." But there is no mention of sinx for arcsinx.
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Even failing this, there still ought at least to be some kind of citation given (even if an explicit proof is inappropriate).
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3118:"The path of integration must not cross ... the imaginary axis in the case of 4.4.3 except possibly inside the unit circle."
3107:{\displaystyle \arctan z\,=\,\int _{0}^{z}{\frac {\mathrm {d} t}{1+t^{2}}}\,=\,{\frac {\pi }{2}}-\operatorname {arccot} z\,.}
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provided that the contour of integration does not cross the part of the imaginary axis which does not lie strictly between -
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2231:. This is not a matter of trigonometry, but rather of your failure to understand the integral notation. For example, in
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3479:, e, and i are all standard according to the ISO. See pages 22&23, 24, and 27 (respectively) of the PDF file at
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Yes a citation to where they are derived is the way to go okay, preferably to something that can be accessed easily.
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which here, means the compositional inverse (the −1 doesn’t mean multiplicative inverse which would be denoted by (
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This is nicely written subsection. That's where
Knowledge shines. I think we should extend such subsections. --
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2045:(if the arc notation is popular and cannot be removed)? Hoping to get a reply in the affirmative... Regards,
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This should be fixed. Knowledge must use common math definitions, esp. standard ones, not introduce new.
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This doesn't appear to be done yet. Here is a diagram that may answer the above concerns for the section
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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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The 4th column in the first table of the section contains typographical errors in rows 4 and 5.
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you have refs to quote). Last but not least, mentioned above inconsistent plots are in place.
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O.K., Now, I’ve got the things you said. I’ll do them as such. As to the notation, the article
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I'm going to go ahead and make the changes. If anyone seriously objects, let me know here.
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Something is going wrong on your end. These all render using Knowledge's backend LaTeX-: -->
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890:{\displaystyle {\frac {x}{\sqrt {1+x^{2}}}}=\tan \theta \cdot \cos \theta =\sin \theta \,.}
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functions deserve their own pages in the Knowledge while their inverse counterparts like
2327:{\displaystyle \arccos x=\int _{x}^{1}{\frac {1}{\sqrt {1-z^{2}}}}\,dz,\qquad |x|\leq 1}
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Solutions to elementary trigonometric equations (≥ 2 questions for editor 9.51.61.147)
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identities in advance of my posting them, please reply here within the next 48 hours.
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2734:) uses the mathematica/nist definition contradicting the article. Very confusing!
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ru:Обсуждение:Безразмерная величина#Единица измерения (?!?) безразмерной величины
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When referring to one of our articles or talk pages, please use ] rather than .
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which may have a different sign than the usual expression. Similarly for arccsc.
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Relationships between trigonometric functions and inverse trigonometric functions
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Relationships between trigonometric functions and inverse trigonometric functions
2889:{\displaystyle \operatorname {arccot}(x)=\arctan \left({\frac {1}{x}}\right)\,.}
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the topics are so closely related that covering them all together works best. –
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between 1966 and whenever they got a website, how is this even up for debate?
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Inverse trigonometric functions#Derivatives of inverse trigonometric functions
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Yes. In the case above, you could put: θ in a corner, 1 on the adjacent side,
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rc- names is that they always remind you that the arc functions give back an
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For the record, only the sine has its own page; the rest are all treated at
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3445:'s, as roman versions are extremely nonstandard. Any thoughts/objections?
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Moreover, in the 4th column of rows 3, 4, 5 it may be questioned whether
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where the square-root function has its cut along the negative real axis;
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This article was the subject of an educational assignment supported by
3220:
And also, if anyone wants to pay $ 160 to see that article, here ya go:
2819:{\displaystyle \operatorname {arccot}(x)={\frac {\pi }{2}}-\arctan(x)\,}
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shows the correct version of the arccotangent. One must choose between
1460:{\displaystyle \operatorname {arccot} z={\frac {\pi }{2}}-\arctan z\,;}
746:{\displaystyle {\sqrt {1+x^{2}}}=\vert \sec \theta \vert =\sec \theta }
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to allow readers to have a choice between merged and unmerged versions
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Knowledge defines arccot to be the inversion of cot on the interval
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Looking back at the old history of this article, it seems as if the
1562:{\displaystyle \operatorname {arccsc} z=\arcsin {\frac {1}{z}}\,.}
1511:{\displaystyle \operatorname {arcsec} z=\arccos {\frac {1}{z}}\,;}
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Explanation of "z" in "Expression as definite integrals" section?
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1341:{\displaystyle \arcsin z=\arctan {\frac {z}{\sqrt {1-z^{2}}}}\,}
3189:< π, or at least it did in 2009. See page 25 of the PDF at
472:{\displaystyle \sin(\arctan x)={\frac {x}{\sqrt {1+x^{2}}}}\,,}
1265:{\displaystyle \arctan z=\int _{0}^{z}{\frac {dz}{1+z^{2}}}\,}
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Inverse trigonometric functions with their OWN WIKIPEDIA PAGE
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678:{\displaystyle 1+x^{2}=1+\tan ^{2}\theta =\sec ^{2}\theta }
381:, which states useful rules without giving any background.
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section. Sorry if this response was too slow to be useful.
2635:{\displaystyle 0.5+(k-{\frac {1}{2}}){\frac {(1-0.5)}{n}}}
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https://www.docuarea.org/home/19852-ISO-80000-2-2019.html
806:{\displaystyle {\frac {1}{\sqrt {1+x^{2}}}}=\cos \theta }
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https://people.engr.ncsu.edu/jwilson/files/mathsigns.pdf
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There's no need to change the article now, but upright d
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https://people.engr.ncsu.edu/jwilson/files/mathsigns.pdf
1403:{\displaystyle \arccos z={\frac {\pi }{2}}-\arcsin z\,;}
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Furthermore: the plot of arccot in the complex plane (
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because θ is in (-π/2, π/2) where secant is positive
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Circular Functions definitions. Formula 4.4.3 says:
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2719:http://www.wolframalpha.com/input/?i=arccotangent
3707:{\displaystyle \arcsin(x),\arcsin(x),\arctan(x)}
3627:{\displaystyle \arcsin(x),\arcsin(x),\arctan(x)}
3257:ru:Обсуждение:Тригонометрические функции#Радианы
2732:https://en.wikipedia.org/File:Complex_ArcCot.jpg
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901:Substituting for θ, we get the desired formula.
4224:Knowledge level-5 vital articles in Mathematics
2096:Talk:Inverse trigonometric functions/Archive 1
406:They are easy to derive. For example, to get
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2024:<< I copied this from my talk page.
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4214:Knowledge vital articles in Mathematics
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600:{\displaystyle x^{2}=\tan ^{2}\theta }
4229:B-Class vital articles in Mathematics
3889:is overspecified in the light of the
7:
2680:{\displaystyle {\frac {(1-0.5)}{n}}}
2098:, for more discussion of this issue.
515:{\displaystyle \theta =\arctan x\,,}
117:This article is within the scope of
60:It is of interest to the following
18:Talk:Inverse trigonometric function
4239:High-priority mathematics articles
3042:
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137:Knowledge:WikiProject Mathematics
4209:Knowledge level-5 vital articles
3932:
3775:we should follow this convention
2757:File:Arctangent Arccotangent.svg
183:
140:Template:WikiProject Mathematics
104:
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3999:Range of usual principal value
3994:Range of usual principal value
3564:Inverse trigonometric functions
1051:History of the sin(x) notation?
1001:is an inverse trig function of
483:one calculates as follows. Let
157:This article has been rated as
4219:B-Class level-5 vital articles
4189:06:14, 28 September 2024 (UTC)
4174:04:46, 28 September 2024 (UTC)
3923:15:31, 18 September 2022 (UTC)
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3166:23:42, 19 December 2020 (UTC)
3151:19:35, 15 December 2020 (UTC)
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1116:00:11, 20 November 2017 (UTC)
258:{\displaystyle \tan(\theta )}
131:and see a list of open tasks.
4234:B-Class mathematics articles
4158:Maybe you’re overscripted?
3965:20:02, 1 February 2023 (UTC)
3913:and the rows 1, 2, 6, 7, 8.
3305:11:28, 17 January 2015 (UTC)
3273:09:03, 17 January 2015 (UTC)
2910:07:20, 11 January 2014 (UTC)
2750:14:26, 10 January 2014 (UTC)
2717:), as well as wolframalpha (
2201:10:46, 12 January 2017 (UTC)
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2127:for the inverse function of
2047:
3796:00:52, 7 October 2020 (UTC)
3761:22:50, 6 October 2020 (UTC)
3733:22:31, 6 October 2020 (UTC)
3716:There is no logic behind it
3311:Inverse cosecant formatting
2697:02:11, 2 October 2013 (UTC)
2222:22:32, 1 October 2013 (UTC)
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3493:01:53, 11 March 2021 (UTC)
3329:21:01, 13 April 2016 (UTC)
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2015:08:28, 17 April 2013 (UTC)
1187:23:41, 14 April 2013 (UTC)
1171:15:38, 14 April 2013 (UTC)
1138:Extension to complex plane
1132:00:07, 11 March 2024 (UTC)
1046:21:06, 14 April 2013 (UTC)
975:02:10, 29 April 2012 (UTC)
945:01:36, 29 April 2012 (UTC)
929:13:24, 25 April 2012 (UTC)
911:07:11, 25 April 2012 (UTC)
401:04:21, 25 April 2012 (UTC)
310:{\displaystyle \arctan(a)}
3991:Domain of for real result
3836:The nice thing about the
3538:Complex logarithmic forms
3238:23:28, 12 June 2022 (UTC)
2715:http://dlmf.nist.gov/4.23
1080:06:45, 14 June 2012 (UTC)
1065:13:28, 13 June 2012 (UTC)
156:
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3826:10:00, 7 July 2021 (UTC)
3505:JonathanHopeThisIsUnique
1098:19:35, 26 May 2015 (UTC)
367:04:02, 28 May 2020 (UTC)
355:relationships between...
347:06:11, 23 May 2020 (UTC)
163:project's priority scale
3943:India Education Program
3740:Trigonometric functions
1144:Syed Wamiq Ahmed Hashmi
278:{\displaystyle \theta }
120:WikiProject Mathematics
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3906:{\displaystyle \iff }
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3882:{\displaystyle k\pi }
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112:Mathematics portal
56:content assessment
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4164:comment added by
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3769:Hi Deacon Vorbis,
3438:{\displaystyle e}
3418:{\displaystyle i}
3371:{\displaystyle i}
3351:{\displaystyle e}
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2713:Whereas NIST (
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936:Sławomir Biały
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359:BlackEyedGhost
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129:the discussion
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4179:
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4171:
4167:
4166:93.229.109.29
4163:
4151:
4149:
4147:
4144:
4140:
4137:
4135:
4133:
4130:
4129:
4126:
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4019:
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4008:
4005:
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3998:
3993:
3990:
3987:
3984:
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3976:
3970:
3968:
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3958:
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3754:
3750:
3749:Deacon Vorbis
3743:
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3467:
3463:
3462:Deacon Vorbis
3459:
3458:
3457:
3456:
3452:
3448:
3447:Deacon Vorbis
3432:
3412:
3404:
3388:
3385:
3365:
3345:
3333:
3331:
3330:
3326:
3322:
3317:
3310:
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3200:
3196:
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1129:
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1124:5.173.127.102
1120:
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989:
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768:
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672:
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466:
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351:
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324:
301:
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249:
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228:
211:
210:
203:
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199:
196:
195:
191:
186:
181:
180:
164:
160:
159:High-priority
154:
151:
150:
147:
130:
126:
122:
121:
113:
107:
102:
100:
97:
93:
92:
88:
84:High‑priority
82:
79:
76:
72:
67:
63:
57:
49:
48:
38:
34:
29:
28:
19:
4160:— Preceding
4157:
4142:
4138:
4131:
4117:
4113:
4106:
4092:
4088:
4082:arccotangent
4081:
4067:
4063:
4056:
4042:
4038:
4031:
4017:
4013:
4006:
3974:
3947:
3941:through the
3931:
3863:
3854:_Angle": -->
3841:
3837:
3835:
3807:
3788:Math&App
3782:
3774:
3725:Math&App
3715:
3561:
3541:
3501:
3485:Toby Bartels
3476:
3474:
3378:'s, and the
3337:
3318:
3314:
3297:
3291:
3288:
3282:
3280:
3254:(in Russian)
3250:
3244:Radian… and
3195:Toby Bartels
3186:
3184:
3169:
3154:
3140:
2736:— Preceding
2729:
2726:
2724:]-π/2,π/2[.
2723:
2712:
2709:
2706:
2643:
2570:
2340:
2210:
2193:83.223.9.100
2187:— Preceding
2184:
2168:
2160:
2153:
2146:
2138:
2132:
2128:
2124:
2123:, too, uses
2079:
2071:
2064:
2057:
2049:
2039:
2023:
2004:
1809:
1571:
1350:
1280:
1276:
1274:
1191:
1150:
1141:
1104:
1054:
1038:
1032:
1029:
1023:
1021:
1018:
1010:
1002:
998:
985:
962:
390:
384:
383:
378:
376:
232:
189:
158:
118:
62:WikiProjects
45:
4132:arccosecant
3831:Arc --: -->
3425:'s and the
2343:=0.5, then
2214:74.10.5.213
2043:the article
134:Mathematics
125:mathematics
81:Mathematics
4198:Categories
4057:arctangent
3988:Definition
3915:Nomen4Omen
3846:Acorrector
3403:WP:MOSMATH
1072:Cesiumfrog
997:The angle
393:Cesiumfrog
317:, what is
4183:jacobolus
4107:arcsecant
4032:arccosine
4001:(degrees)
3996:(radians)
3779:MathWorld
3720:MathWorld
3524:JRSpriggs
3265:De Riban5
3120:JRSpriggs
2942:JRSpriggs
2902:JRSpriggs
2689:JRSpriggs
2103:JRSpriggs
2026:JRSpriggs
2007:JRSpriggs
1179:JRSpriggs
1163:JRSpriggs
967:JRSpriggs
903:JRSpriggs
229:Parameter
202:Archive 1
50:is rated
4162:unsigned
3957:PrimeBOT
3545:Rickhev1
3358:'s, the
3321:Jason B.
3259:, &
3251:see also
3246:category
2738:unsigned
2189:unsigned
2020:Notation
1154:contribs
1108:Jim77742
339:SDSpivey
337:called?
190:Archives
4007:arcsine
3644:tangent
2710:]0,π[.
385:Ideally
161:on the
52:B-class
4141:= csc(
4116:= sec(
4091:= cot(
4066:= cot(
4041:= cos(
4016:= sin(
3819:(talk)
3757:videos
3753:carbon
3690:arctan
3672:arcsin
3654:arcsin
3640:cosine
3610:arctan
3592:arcsin
3574:arcsin
3091:arccot
3008:arctan
2858:arctan
2840:arccot
2800:arctan
2769:arccot
2721:) use
2687:. OK?
2353:arccos
2241:arccos
1827:arcsec
1589:arcsin
1539:arcsin
1527:arccsc
1488:arccos
1476:arcsec
1444:arctan
1419:arccot
1387:arcsin
1362:arccos
1306:arctan
1294:arcsin
1204:arctan
1090:Tfr000
1057:Tfr000
1019:Best,
499:arctan
425:arctan
293:arctan
58:scale.
3963:) on
3832:Angle
2642:and d
2159:Hαsнм
2070:Hαsнм
2037:: -->
2036:: -->
1279:and +
1005:, or
526:then
39:This
4170:talk
3982:Name
3961:talk
3919:talk
3850:talk
3792:talk
3729:talk
3642:and
3636:sine
3549:talk
3528:talk
3518:See
3509:talk
3489:talk
3466:talk
3451:talk
3325:talk
3269:talk
3263:… --
3234:talk
3199:talk
3177:talk
3162:talk
3147:talk
3124:talk
2973:talk
2946:talk
2924:talk
2906:talk
2830:and
2746:talk
2693:talk
2227:See
2218:talk
2197:talk
2107:talk
2030:talk
2011:talk
1183:talk
1167:talk
1148:talk
1128:talk
1112:talk
1094:talk
1076:talk
1061:talk
1009:1 +
971:talk
941:talk
925:talk
921:Dmcq
907:talk
397:talk
363:talk
343:talk
153:High
4186:(t)
3955:by
3945:.
3815:NOV
3812:AXO
3300:τlk
2666:0.5
2621:0.5
2581:0.5
2546:0.5
2511:0.5
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