       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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