# Talk:Atan2

WikiProject Mathematics (Rated C-class, Mid-importance)
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Mathematics rating:
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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)

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

## Closed/semi-open interval

It is not the first time I see someone changing $(-\pi,\pi]$ for $[-\pi,\pi]$ 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

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

It couldn't be $-\pi$ because:

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

Therefore atan2's codomain is $(-\pi,\pi]$, NOT $[-\pi,\pi]$. 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

$atan2\left(\pm0,0\right)= atan2\left(\lim_{\;y\rightarrow 0^\pm} y,0\right) = \lim_{\;x\rightarrow 0^\pm} atan2(y,x)$

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

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)