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
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- 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., fourth and first quadrants, | > while our point (-2, 1) is in the third quadrant. But we can conveniently | > 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 |