Over the symmetric interval

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Over the symmetric interval −π3≤θ≤π3-\dfrac{\pi}{3}\le\theta\le \dfrac{\pi}{3}, let A1A_1 be the area enclosed by r=1+2cos⁡θr=1+2\cos\theta and let A2A_2 be the area enclosed by r=1r=1. Determine, to the nearest tenth of a percent, the percentage difference ∣A1−A2∣A2×100%\dfrac{|A_1-A_2|}{A_2}\times 100\%.

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