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Re: Possible Bug in ArcTan ?

• To: mathgroup at smc.vnet.net
• Subject: [mg64798] Re: Possible Bug in ArcTan ?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Thu, 2 Mar 2006 21:46:53 -0500 (EST)
• References: <du6o44$5rg$1@smc.vnet.net> <du83m5$sv3$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote:
> Hi,
>
> why can ArcTan[] have two arguments ArcTan[x,y]

As the Help Browser says,
"taking into account which quadrant the point (x,y) is in."

For example, suppose you want to convert -2 + I to polar form,
r*E^(I*theta). One can't simply say theta = ArcTan[1/-2]. The range of the
single-argument ArcTan is [-Pi/2, Pi/2], i.e., fourth and first quadrants,
while our point (-2, 1) is in the third quadrant. But we can conveniently
say theta = ArcTan[-2, 1].

Note: Some other languages implement the two-argument form under the
name ATAN2. Furthermore, the order of the two arguments is often backwards
compared to Mathematica's, that is, ATAN2(y,x).

David