Mathematics

Problem

Over the symmetric interval

-\dfrac{\pi}{3}\le\theta\le \dfrac{\pi}{3}

, let

A_1

be the area enclosed by

r=1+2\cos\theta

and let

A_2

be the area enclosed by

r=1

. Determine, to the nearest tenth of a percent, the percentage difference

\dfrac{|A_1-A_2|}{A_2}\times 100\%