RE: Two Argument ArcTan Function
- To: mathgroup at smc.vnet.net
- Subject: [mg42783] RE: [mg42778] Two Argument ArcTan Function
- From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
- Date: Fri, 25 Jul 2003 11:54:52 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
>-----Original Message----- >From: David Park [mailto:djmp at earthlink.net] To: mathgroup at smc.vnet.net >Sent: Friday, July 25, 2003 11:09 AM >To: mathgroup at smc.vnet.net >Subject: [mg42783] [mg42778] Two Argument ArcTan Function > > >Dear MathGroup, > >The two argument function, ArcTan[x,y], is a very nice function and >Mathematica knows how to do a lot with it. But sometimes it is >difficult to >bring it into play without just typing it in. > >Consider the case of inverting polar coordinates. > >eqns = {x == r Cos[t], y == r Sin[t]}; >Solve[eqns, {r, t}, {x, y} \[Element] Reals] // Simplify > >If we discard the two negative r solutions, we obtain two solutions >involving ArcCos. But couldn't we have a single solution using >ArcTan[x,y]? >I'm curious to know if there is a method to get Mathematica to >produce that >solution? > >David Park >djmp at earthlink.net >http://home.earthlink.net/~djmp/ > > Dear David, if you have cartesian coordinates defined (symbolically) as In[1]:= {x, y} = r{ Cos[t], Sin[t]} ; then you may revert (symbolically) to polar with In[11]:= FullSimplify[{Sqrt[{x, y}.{x, y}], ArcTan[x, y]}, {Positive[r], t \[Element] Reals}, TransformationFunctions -> {Automatic, TrigToExp, PowerExpand}] Out[11]= {r, t} (It also works with assuption r \[Element] Reals (but I hate that). Of course numerical work is easier. -- Hartmut