# Talk:Atan2

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Field:  Geometry

## Order of arguments

This article isn't very clear about the order of the two arguments x and y in the atan2() function call. Many people will incorrectly assume at first glance that it is atan2(x,y) -- the text should be more explicit (I missed the order in the "more specifically" text the first 3 times I read it). I maintain a parser for an expression language where atan2(a,b) returns atan(b/a) rather than C's atan(a/b)...

Fixed. ~a (usertalkcontribs) 00:22, 31 March 2007 (UTC)

The C-language atan2 is convenient to apply by remembering that tangent = opposite/adjacent. Since angle = atan2(opposite,adjacent), it's easy to remember. Hollimb 18:43, 25 March 2007 (UTC)

## The first note under "Definition"

The first note under the section "Definition" read to the effect that adding 2π to a result in the range (-π,π] resulted in the range (0,2π], which doesn't seem correct. I've changed it to read that adding π has this effect, and have further clarified the line to reduce potential ambiguity regarding to which value the additional π is added.198.54.202.94 (talk) 17:52, 28 May 2008 (UTC)

${\displaystyle {\frac {\sin(\theta +\pi )}{\cos(\theta +\pi )}}={\frac {\sin(\theta )}{\cos(\theta )}}=\tan(\theta )\,}$
But
${\displaystyle {\mbox{atan2}}(\sin(\theta +\pi ),\cos(\theta +\pi ))\neq {\mbox{atan2}}(\sin(\theta ),\cos(\theta ))\,}$
--Bob K (talk) 23:24, 28 May 2008 (UTC)

## Closed/semi-open interval

It is not the first time I see someone changing ${\displaystyle (-\pi ,\pi ]}$ for ${\displaystyle [-\pi ,\pi ]}$ in the first paragraph (Indeed, I think I did so sometime in the past). I think this issue should be discussed here and an invisible comment should be kept in the article, for editor's guidance.

As a mathematical funcion, atan2 is defined as

${\displaystyle \operatorname {atan2} (y,x)={\begin{cases}\arctan({\frac {y}{x}})&\qquad x>0\\\pi +\arctan({\frac {y}{x}})&\qquad y\geq 0,x<0\\-\pi +\arctan({\frac {y}{x}})&\qquad y<0,x<0\\{\frac {\pi }{2}}&\qquad y>0,x=0\\-{\frac {\pi }{2}}&\qquad y<0,x=0\\{\text{undefined}}&\qquad y=0,x=0\\\end{cases}}}$

It couldn't be ${\displaystyle -\pi }$ because:

• ${\displaystyle y<0\implies \arctan({\frac {y}{x}})\neq 0\implies atan2(y,x)>-pi}$
• ${\displaystyle y>0\implies atan2(y,x)>0}$
• ${\displaystyle y=0\land x>0\implies atan2(y,x)=0}$
• ${\displaystyle y=0\land x<0\implies atan2(y,x)=pi}$
• ${\displaystyle y=0\land x=0\implies \implies atan2(y,x)undefined}$

Therefore atan2's codomain is ${\displaystyle (-\pi ,\pi ]}$, NOT ${\displaystyle [-\pi ,\pi ]}$. I think the confusion arises from computational implementation and how it deals with signed zero.

Since "zero" is now a limit instead of finite real value, we have

${\displaystyle atan2\left(\pm 0,0\right)=atan2\left(\lim _{\;y\rightarrow 0^{\pm }}y,0\right)=\lim _{\;x\rightarrow 0^{\pm }}atan2(y,x)}$

and, particularly ${\displaystyle \lim _{\;x\rightarrow 0^{-}}atan2(y,x)=-\pi }$

but this is only a limit; mathematical atan2 function does NEVER gives that result. Rjgodoy 19:27, 3 July 2007 (UTC)

## atan2 and atan

In Maxima atan2(x,1)=atan(x)

Adam majewski 21:02, 28 October 2007 (UTC)

Hi, I'm not sure where this link shall point out so I may put it here if someone knows how to fix it. There's a broken link in reference [1] where it says:

include the C-style atan2 function. The Linux Programmer's Manual [1] says:

--Felipebm (talk) 19:08, 25 March 2008 (UTC)

Neither I do, but IA-32 Intel® Architecture Software Developer’s Manual. Volume 2A: Instruction Set Reference, A-M, 2004 should include a definition too. We could use it instead of The Linux Programmer's Manual. Rjgodoy (talk) 01:33, 26 March 2008 (UTC)

## Graph Incorrect?

I don't understand why the 3D graph shows a slight curve in the profile visible along the negative x. Shouldn't the graph be a constant value of pi along here? —Preceding unsigned comment added by 198.99.123.63 (talk) 16:37, 10 April 2008 (UTC)

Actually it should be -pi/2. However there is no such a slight curve! After your comment I became very suspicious about the graph and plotted the surface by myself (thus I could verify that the values alongside x axis were correct and constant either -pi/2 or pi/2, but for x=0 y=0 of course). It seems to be a slight curve because of an optical illusion due to the perspective and the slight pendient wrt. y axis. Rjgodoy (talk) 21:35, 10 April 2008 (UTC)

The graph is nice but this graph has no axis labels. I don't suppose it means much to you as you know what the graph is saying but anyone like me who is not 100% sure would appreciate people sticking to the good old rule of labeling each and every axis in every graph ever. —Preceding unsigned comment added by 132.181.15.75 (talk) 22:16, 28 May 2008 (UTC)

The chart showing atan2 is completely wrong. I just plotted it in Excel. —Preceding unsigned comment added by 142.23.221.132 (talk) 01:36, 3 February 2009 (UTC)

Did you note the statement in the article that Excel has the two arguments reversed? — Carl (CBM · talk) 02:36, 3 February 2009 (UTC)

## Sign of output

The article states that the results are positive for y>0 and negative for y<0, but what about y=0? AFAICT, y<0 either gives 0 or π, so it should read that the results are positive for y>=0 and negative for y<0.--Subversive Sound (talk) 14:57, 9 July 2010 (UTC)

The full definition is given later on, that's a very general idea of how angles are measured. You'd have people saying 0 isn't positive with the change you say. Dmcq (talk) 15:20, 9 July 2010 (UTC)

## More stable/consistent 'non-condition' formula?

Is there maybe a more convoluted formula that doesn't require any conditions, but is also computationally stable and isn't often undefined when y=0 (or at least the latter) ? I think this would merit inclusion into the article. --Skytopia (talk) 22:32, 5 September 2010 (UTC)

## Derivative

In my opinion the section called "Derivative" uses needless complicated formulation, as if some finds such things interesting. As atan2 is a function of two variables, it suffices to just give both the partial derivatives. Nijdam (talk) 20:14, 12 November 2011 (UTC)

Yes the derivation is totally unnecessary. Dmcq (talk) 20:59, 12 November 2011 (UTC)

## Quality

I first noticed this article existed in 2007 and didn't find it noteworthy but still pointed traffic it's way, since then it has greatly improved! -- BlindWanderer (talk) 06:54, 28 October 2012 (UTC)

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## section: Definition and computation

I do not understand the following (at the end of the section):
"Computation gives

${\displaystyle {\text{atan2}}(y,x)=\left({-y \over x^{2}+y^{2}},\ {x \over x^{2}+y^{2}}\right)\ .}$"
1. I do not see a computation.
2. In the foregoing definition and statements atan2(y,x) delivers a real (scalar). How can it deliver a 2-dim point ? and
3. especially this one ?

Can somebody help me ? --Nomen4Omen (talk) 20:24, 26 January 2017 (UTC)

Thanks for spotting that. This seems to have gotten lost in translation somewhere. This older version (from almost a year ago) makes significantly more sense. I'm going to see what I can do to fix this. --♫CheChe♫ talk 19:34, 27 January 2017 (UTC)
Fixed. --♫CheChe♫ talk 19:47, 27 January 2017 (UTC)

## Section: Derivative

Up to my knowledge

${\displaystyle \nabla {\text{atan2}}(y,x)=\left({x \over x^{2}+y^{2}},\ {-y \over x^{2}+y^{2}}\right)}$

is not the divergence, but is the gradient of atan2.

(Nabla is OK.) --Nomen4Omen (talk) 14:46, 30 January 2017 (UTC)

Yikes! My mistake. Slip of the tongue there, divergence is a scalar, so it can't be that (though I'm glad the equation says the right thing). --♫CheChe♫ talk 15:24, 30 January 2017 (UTC)
Ok, that should be fine now. Thanks for the help. --♫CheChe♫ talk 15:29, 30 January 2017 (UTC)