Convert function from polar to Cartesian
- To: mathgroup at smc.vnet.net
- Subject: [mg112754] Convert function from polar to Cartesian
- From: Sam Takoy <sam.takoy at yahoo.com>
- Date: Wed, 29 Sep 2010 04:14:49 -0400 (EDT)
Hi,
I've stumbled onto an unexpected problem. I have a function in polar
coordinate and I need to convert it to Cartesian coordinates:
fPolar[r_, a_] = r^2 Cos[2 a];
fCart[x_, y_] = fPolar[Sqrt[x^2 + y^2], ArcTan[x, y]];
fCart[x, y]
I get: (x^2 + y^2) Cos[2 ArcTan[x, y]].
But how to get rid of the ArcTan[x, y]? I've tried this:
fCart[x, y] //
TrigExpand /. {Cos[ArcTan[x, y]] -> x/Sqrt[x^2 + y^2],
Sin[ArcTan[x, y]] -> y/Sqrt[x^2 + y^2]}
but it does not do the substitution I need it to do. So what's the
proper way to get rid of the ArcTan[x, y] and for the simple example
above, to obtain x^2 - y^2?
Many thanks in advance,
Sam