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How do I approach this problem?

Graph the following polar curve and show that it cuts out 5 different regions. Find the area of each of those regions.

$r=1+6\sin(\theta)+\cos(6\theta)$

Also, find the arc length (numeric value) for each of the loops of this (the unfolded) graph.

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    @jeffq: Have you got the answer yet?2012-11-24

2 Answers 2

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You need to look at which curve is outside and which is inside in each sector. Remember that area in polar coordinates is given by $1/2\int r^2 \, d\theta$.

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Here is the graph for theta in $[0,2\pi].$

enter image description here