Plot Inequality Area of polar equation? Using Wolfram Alpha or Matlab?

I want to plot or graph the inequality area between two polar equations.

For example, I'd like to plot the area between $\displaystyle r = 3 \sin \theta$ and $\displaystyle r = 4 \sin \theta$.

I am very familiar with both Matlab and Wolfram Alpha, however I can't figure out how to do this. Any suggestions?

Re: Plot Inequality Area of polar equation? Using Wolfram Alpha or Matlab?

Quote:

Originally Posted by

**VinceW** I want to plot or graph the inequality area between two polar equations.

For example, I'd like to plot the area between $\displaystyle r = 3 \sin \theta$ and $\displaystyle r = 4 \sin \theta$.

I am very familiar with both Matlab and Wolfram Alpha, however I can't figure out how to do this. Any suggestions?

Construct an indicator variable which is $\displaystyle 1$ in the area in question and $\displaystyle 0$ elsewhere on a $\displaystyle r, \theta$ grid (or $\displaystyle x,y$ grid if you prefer). Now do a density plot (a colour 3D plot looking down from above) of the indicator variable.

CB