Re: Possible Bug in ArcTan ?

• To: mathgroup at smc.vnet.net
• Subject: [mg64894] Re: Possible Bug in ArcTan ?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Tue, 7 Mar 2006 06:11:44 -0500 (EST)
• Organization: The University of Western Australia
• 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> <due86a\$9vj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <due86a\$9vj\$1 at smc.vnet.net>,
"Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote:

> 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.

There is no "division by zero" error using the form

2 ArcTan[y/(x+Sqrt[x^2+y^2])]

except when x == y == 0 -- where the result is undefined anyway.
However, as David Cantrell points out, this form (only) fails if y is
zero and x is negative (returning 0 instead of Pi), and so must be
considered separately.

Since Mathematica has the two-argument form, one should use it. However,
my point was that, mathematically, 2 ArcTan[y/(x+Sqrt[x^2+y^2])] is
preferable to ArcTan[y/x].

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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