       Re: Shade area between two polar curves

• To: mathgroup at smc.vnet.net
• Subject: [mg100201] Re: Shade area between two polar curves
• From: Helen Read <hpr at together.net>
• Date: Thu, 28 May 2009 04:27:00 -0400 (EDT)
• References: <gvhma6\$83c\$1@smc.vnet.net>
• Reply-to: read at math.uvm.edu

```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?

Something like this?

r[t_] = 1 + 2 Cos[t];
s[t_] = 2;
plot1 = PolarPlot[{r[t], s[t]}, {t, 0, 2 \[Pi]}, PlotStyle -> Thick];
plot2 = ParametricPlot[{u r[t] Cos[t], u r[t] Sin[t]}, {u, 0,
1}, {t, -\[Pi]/3, \[Pi]/3},
RegionFunction -> Function[{x, y, u, t}, u r[t] > s[t]],
Mesh -> None];
Show[{plot1, plot2}, PlotRange -> Automatic]

--
Helen Read
University of Vermont

```

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