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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


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