The cardioid is given by the equation for .

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

Problem

The cardioid is given by the equation r=3 (1+cos⁡θ)r=3\,(1+\cos\theta) for 0≤θ≤2π0\le\theta\le2\pi. (a) Verify that the curve passes through the pole (origin) and identify the angle(s) at which this occurs. (b) Calculate the exact area enclosed by the entire cardioid.

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