       Re: Possible Bug in ArcTan ?

• To: mathgroup at smc.vnet.net
• Subject: [mg64832] Re: Possible Bug in ArcTan ?
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Sun, 5 Mar 2006 03:18:50 -0500 (EST)
• Organization: Uni Leipzig
• References: <du6o44\$5rg\$1@smc.vnet.net> <du83m5\$sv3\$1@smc.vnet.net> <du8are\$fp7\$1@smc.vnet.net> <dubgv0\$fm7\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Paul,

why you want avoid the two-argument form. The two-argument form help
a lot during programing, because one has not to type

If[x=!=0,ArcTan[y/x]]

and a division by zero is in the most programing languages
a very hard and evil error.

Regards
Jens

"Paul Abbott" <paul at physics.uwa.edu.au> schrieb im
Newsbeitrag news:dubgv0\$fm7\$1 at smc.vnet.net...
| In article <du8are\$fp7\$1 at smc.vnet.net>,
| "David W. Cantrell" <DWCantrell at sigmaxi.org>
wrote:
|
| > "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.,
| > while our point (-2, 1) is in the third
| > say theta = ArcTan[-2, 1].
|
| Or we can say theta = 2 ArcTan[1/(Sqrt-2)]
(see below).
|
| > 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).
|
| There is another way that avoids the
two-argument form altogether. Using
| the half-angle formula for tan,
|
|  Simplify[Tan[t/2] == Sin[t]/(Cos[t] + 1)]
|
|  True
|
| then in polar coordinates, x=r Cos[t], y=r
Sin[t], r=Sqrt[x^2+y^2],
|
|  Tan[t/2] == y/(x+r) ==> t == 2
ArcTan[y/(x+Sqrt[x^2+y^2])]
|
| This formula is also valid when x == 0, whereas
ArcTan[y/x] is
| problematic there (ArcTan[0,y] is ok, of
course).
|
| Cheers,
| Paul
|
|
_______________________________________________________________________
| Paul Abbott
Phone:  61 8 6488 2734
| School of Physics, M013
Fax: +61 8 6488 1014
| The University of Western Australia
(CRICOS Provider No 00126G)
| AUSTRALIA
http://physics.uwa.edu.au/~paul
|

```

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