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The two Cartesian coordinates x and y can be converted to the two polar coordinates r and θ by using the trigonometric functions sine and cosine:
while the two polar coordinates r and θ can be converted to the Cartesian coordinates x and y by
Isn't this the wrong? Shouldn't it be:
The two Cartesian coordinates x and y can be converted to the two polar coordinates r and θ by using the Pythagorean theorem and the trigonometric function cosine:
while the two polar coordinates r and θ can be converted to the Cartesian coordinates x and y by
CJ Drop me a line! • Contribs 15:16, 12 May 2011 (UTC)
This is wrong. Talk to any mathematician, and (s)he will tell you that y=rsin(theta), x=rcos(theta), and that x^2+y^2=r^2 In addition, r=(y/sin(theta));r=(x/cos(theta));r=(sqrt(x^2+y^2)) and theta=arctan(y/x); theta=arctan(y/x+pi);theta=arctan(y/x-pi) (In addition, theta=(pi/2) if and only if y=0, and theta=0 if and only if x=0) It's very basic Calculus user:998walrus 1 March 2012 22:15
This article has been edited by a user who is known to have misused sources to unduly promote certain views (see WP:Jagged 85 cleanup). Examination of the sources used by this editor often reveals that the sources have been selectively interpreted or blatantly misrepresented, going beyond any reasonable interpretation of the authors' intent.
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I searched the page history, and found 3 edits by Jagged 85 (for example, see this edits). Tobby72 (talk) 21:00, 16 January 2012 (UTC)
Would someone kind enough to edit all the theta to phe which supposed to be the ISO standard for Azimuth Angle? Even though a lot of vector calculus & general physics textbooks use the former one. (Theta) It would make most students life less miserable. — Preceding unsigned comment added by 218.238.173.141 (talk) 14:26, 25 March 2012 (UTC)
Well I didn't know that the Azimuth Angle wasn't allowed in xy-plane 2D only space. Azimuth angle was used there on celestial coordinate system in Azimuth wiki article which was linked from Spherical coord wiki article; that's where I read it. It's just that some commonly used cylindrical system(phe for angle projected on xy-plane between xz ref plane through origin and another vertical plane through origin) & spherical system(phe for angle on xy-plane as well) are analogous to the polar coordinate system. Not very conform at all to use different variables for the same rotation. My old Calculus book by the way used theta for Azimuth angle & phe for angle from z axis with origin as pivot. One more thing I don't get is that on Vector Calculus part of the article it used cross product with one of the vector k normal to the projection plane! That involves z axis. Shouldn't that justify phe instead of theta? Also the term azimuth was used in the last sentense of the Introduction.— Preceding unsigned comment added by 218.238.173.141 (talk) 15:46, 25 March 2012 (UTC)
Actually No it(azimuth angle article) didn't say related to Polar coordinate it did relate itself to the spherical system though. I had no idea as well about ISO standard to some math coordinate system. But after looking at the spherical system wiki article under subtitle "Conventions" there is another article link of ISO 33-11 which is pretty convincing that there is made standard. Maybe these are too commonly used. And yes, haven't seen any programming language using degree in trig functions. Maybe maple if you can call that a programming language. By the way, I can keep the variables as before, no big deal. I was just checking r double primes(t) calculation in each coordinate system especially spherical coord and wiki's spherical coordinate & cylindrical coordinate had switched theta & phe. And reason being this way was you know why(Standardization of dummy variables. I don't get it.
Yes, I agree with a lot of what yall said. Using phi would certainly be more intuitive. After all, polar coordinates are a special case of cylindrical coordinates (for when z=0) and suddenly switching from "phi" to "theta" for the azimuthal angle is confusing. Also, it is true that "phi" is the ISO 31-11 standard, so shouldn't we be following it in this article? Let me know if you guys agree, and I'd be happy to change it! Monsterman222 (talk) 21:23, 12 October 2012 (UTC)
So, I haven't heard back from anyone in half a year... Should I go ahead and change "theta" to "phi" to conform with ISO 31-11? (which, by the way, the article on the spherical coordinate system also uses) Monsterman222 (talk) 06:51, 25 March 2013 (UTC)
I've converted the article to phi. Could anyone help by updated the images? Monsterman222 (talk) 09:22, 23 April 2013 (UTC)
In mathematics the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the anticlockwise angle between the positive x-axis and the projection of the vector onto the xy-plane. The angle is the same as an angle in polar coordinates of the component of the vector in the xy-plane and is normally measured in radians rather than degrees. As well as measuring the angle differently, in mathematical applications theta, , is very often used to represent the azimuth rather than the symbol phi .
Well, right now, this bit is confusingly flipping back and forth between symbols ϕ & :
There is no ϕ in the graphic at the right. One assumes the symbol should be the same throughout, rather than using one symbol in the description and another in the equations and/or graphic?? If so, can we get the symbol usage consistent, please? Currently I'm trying to figure something out and this is making it 'Greek to me...' 50.53.112.40 (talk) 06:25, 15 July 2015 (UTC)
An interesting technicality is whether there is a "standard" polar coordinate system and, if so, does it specify that the radius r must be non-negative? Clearly one can make sense of an expression like r cos(theta) if r is negative and convert such an (r,theta) to a cartesian coordinate (x,y). However, converting the point (x,y) back to a polar coordinate by the usual method would produce a point where r was positive.
I see nothing that prevents a "polar equation" from having a negative r value. So I wonder if polar equations are required to produce "standard" polar coordinates or whether they merely produce numbers than can be converted to standard polar coordinates.
Perhaps the people that know about the "chart and atlas" treatment of coordinate systems for manifolds can comment on whether there is a standard polar coordinate system.
Tashiro (talk) 19:38, 2 April 2012 (UTC)
I'm curious whether there is any formal mathematical definition for "standard" polar coordinates. I agree that what one usually does when computing the polar coordinates of a point is compute r as positive and theta as (-pi, pi). But is this the "standard" way only in the sense of a social behavior or is there a formal mathematical definition of a system of polar coordinates that defines this standard?
If we allow the same point to be represented by several different pairs of numbers of the form (r, theta) then technically we should avoid statements that imply there is only one representation. For example, we shouldn't say that we are presenting "the" formulas for finding "the" polar coordinates of a point whose cartesian coordinates are (x,y). Instead we should say we are presenting "some" formulas for finding "a" polar coordinate of a point whose cartesian coordinates are (x,y). ( Of course, I suspect any attempt to reform this habitual language will fail!) — Preceding unsigned comment added by Tashiro (talk • contribs) 07:08, 3 April 2012 (UTC)
I don't mean something like an ISO standard. I mean some established and precise definition within the field of mathematics, such as the definition of "Abelian group" or "vector space", which are not (as far as I know) ISO standards.
An example of my quibble about language is the passage in the current article that says "while the Cartesian coordinates x and y can be converted to the polar coordinates r and θ by:
r = \sqrt{y^2 + x^2} ..."
It would be clearer not to say "the polar coordinates". It could say "a polar coordinate" or "one pair of polar coordinates for the point (x,y)" given that the article takes the viewpoint that polar coordinates are not unique.
Tashiro (talk) 21:32, 3 April 2012 (UTC)
I'm not disputing that that part of the article gives the usual formulae ( my example refers to the formulae, not the definition). My original question is whether there is a mathematical definition that defines the unique pair of numbers produced by those formulas as the "standard" or "normal" polar coordinates. As an analogy, an inverse trig like y = arcsin(x) isn't defined merely by the formula sin(y) = x since this doesn't define a unique value of y. To define arcsin(x) we can specify a definite range for y, but there is (or used to be, when I was in school) an alternative technical terminology about "principal" angles that we can use instead of specifying the range. So I am wondering if there is a similar terminology for the polar coordinates produced by those formulae. Is "standard" or "normal" a technical term in the same sense that "principal angle" is a technical term? (I don't know the answer to this legalistic question. I'm just asking!)
My point about the text surrounding the formulae is merely that the phrase "can be converted to the polar coordinates" could be changed to "can be converted to a pair of polar coordinates" in order to emphasize that the pair of coordinates produced by the formulae is not the only pair of polar coordinate for (x,y).
Tashiro (talk) 16:11, 8 April 2012 (UTC)
I could write something about this topic if someone thinks it could be useful / is not covered anywhere. Note that when i was studying this sort I thing i was unable to find any reference online (except for some research articles). --Agi 90 (talk) 11:48, 1 June 2012 (UTC)
I am not sure if it is a space or a variation on the polar coordinates. For instance, using the notation (r, theta) for a point, the point (r0, theta) != (ro, theta+2*pi). Hence the plane/space/coordinate system is sort of a spiral. What is this called? — Preceding unsigned comment added by 68.228.41.185 (talk) 08:25, 1 November 2012 (UTC)
This article is full of short paragraphs and sections and is, for the most part, devoid of inline citations. In addition, the intro is very short and the prose contains some awkwardly constructed sentences. Though I won't nominate it for an FAR right now, I don't believe it meets the 2014-era FA criteria. Tezero (talk) 02:47, 27 July 2014 (UTC)
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Regardless to whom WP:BRD applies, I enjoy repeating the facts, given already in my edit summary.
No rational reasoning for using "" instead was given yet. Purgy (talk) 07:41, 17 September 2018 (UTC)
I tried to (re-)state my opinion on this ridiculous quarrel about captioning one letter in my above OP, and expected some, at least semi-, professional argumentation against it. Instead, the IP rebuffs my statement with mathematical ignorance and bureaucratic, and imho incoherent, application of WP-rules, seriously suggesting to remove all my(!) improvements as a solution.
I am not interested in lowering my bar to this level. Purgy (talk) 07:08, 18 September 2018 (UTC)
It is conventional within mathematics to denominate the angle in radians, and to diagram polar coordinates by placing the zero angle along the positive abscissa, with increasing angles progressing counterclockwise.
Half a math degree thirty years ago, and this is now the best I can do. :-( But at least I know what needs to be said, if not necessarily how to best say it.
Likely this would benefit from some fine tuning. (Note also, I wasn't able to lift optimal text from the radians article on scant inspection, so there's a potential edit there, too.) — MaxEnt 22:31, 13 February 2019 (UTC)
Hi editors, as part of WP:URFA/2020 I reviewed this article and I do not believe it meets the featured article criteria anymore. I am concerned that there are multiple uncited sentences and paragraphs throughout the article, and the "General references" section should be used as footnotes throughout the article. Is anyone interested in bringing this back to FA quality? Z1720 (talk) 22:47, 10 April 2021 (UTC)
Should Christoffel symbols be added?
Angulon (talk) 01:25, 25 January 2023 (UTC)
Proof of x= r×cos×phi Etc. Yuthfghds (talk) 16:07, 27 May 2023 (UTC)
The folium of Descartes is another nice application of polar coordinates and should perhaps be included in this article. Kontribuanto (talk) 21:18, 22 April 2024 (UTC)