Talk:Atan2

I m' not used to formula editing. Were it the case, I would fix the bit myself.

Anyway, in the definition of the function atan2, the first case appears to involve the function atan2 itself! This recursive definition being improper here, I assume the canonical "arctan" function was meant. Max.

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 (user • talk • contribs) 00:22, 31 March 2007 (UTC)[reply]

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)[reply]

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\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 $-\pi$ because:

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

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

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

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)[reply]

atan2 and atan

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

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

broken link

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)[reply]