Let , , and be three polar curves on defined respectively by , , and . Rank the areas…

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

Problem

Let RR, SS, and TT be three polar curves on 0≤θ≤π0\le \theta \le \pi defined respectively by r=sin⁡θr=\sin\theta, r=12+sin⁡θr=\dfrac12+\sin\theta, and r=1+sin⁡θr=1+\sin\theta. Rank the areas ARA_R, ASA_S, and ATA_T enclosed by the curves from least to greatest. (a) AS<AR<ATA_S < A_R < A_T (b) AR<AS<ATA_R < A_S < A_T (c) AR=AS=ATA_R = A_S = A_T (d) AR<AT<ASA_R < A_T < A_S

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