The graph of the polar curve traces a symmetrical petal–shaped region.
MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
The graph of the polar curve r=4sinθ traces a symmetrical petal–shaped region.
(a) Determine an interval of θ on which the curve completes exactly one petal and explain your reasoning.
(b) Calculate the exact area of that single petal.
(c) The curve is rotated about the initial ray to generate all of its petals. Find the total exact area enclosed by the entire curve.