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Consider the region contained inside both the cardioid $r=1+\cos\theta$ and outside the circle $r=3\cos\theta$, where $r$ and $\theta$ are polar coordinates. So weirdly enough I know how to calculate the area itself, but the question wants me to define the domain of this region in terms of polar coordinates???

Since I have two distinct regions, one above and one below the axis, how could I define the domain? I was thinking of using union/intersection but it didn't work. Thanks

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Equate r.

$$ 3\, c = c, c = cos \, \theta =\frac12, \theta = \pm (\pi/3 ) , $$ which is the domain symmetric to x axis.

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  • $\begingroup$ What about r? I know it's not just from 3 cos theta to 1+cos theta $\endgroup$ – NDTB Apr 25 '16 at 5:39
  • $\begingroup$ The r is between 0 and 3/2., outer lune area. You should be looking at the intersection points , ie., their range and domains. Your region of interest is double this, symmetric to z axis. $\endgroup$ – Narasimham Apr 25 '16 at 6:11

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