Re: Re: Shade area between two polar curves

*To*: mathgroup at smc.vnet.net*Subject*: [mg100236] Re: [mg100218] Re: Shade area between two polar curves*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 28 May 2009 19:35:05 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <gvhma6$83c$1@smc.vnet.net> <200905281049.GAA19261@smc.vnet.net>*Reply-to*: murray at math.umass.edu

Of course Cos[t] and 1/Sqrt[1+Tan[t]^2] do NOT have the same values over their entire domains, e.g., for Pi/2 < t < 3 Pi/2. So one must be careful if going from polar to cartesian coordinates in order to apply a RegionPlot for filling a PolarPlot. All of this begs the question as to why PolarPlot and ParametricPlot don't have a Filling option! dh wrote: > Hi Chee, > > try RegionPlot. Remember that Cos[t]=1/Sqrt[1+Tan[t]^2]: > > ============================== > > f[x_, y_] := > > 1 + 2/Sqrt[1 + y^2/x^2] > Sqrt[x^2 + y^2] && Sqrt[x^2 + y^2] > 2 > > > > RegionPlot[f[x, y], {x, 0, 3}, {y, -2, 2}] > > ================================= > > Daniel > > > > Chee Lim Cheung wrote: > >> Hi All > > >> I have plotted two graphs using PolarPlot, namely the limacon r=1+2 cos(t) > >> and the circle r = 2 from t = 0 to t = 2 Pi. and I wish to shade the area > >> inside the limacon but outside the circle. Can anyone suggest a way to do > >> it? > > >> Thanks and Regards > >> Chee > > > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Re: Shade area between two polar curves***From:*dh <dh@metrohm.com>