A rose curve is defined by for .

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

Problem

A rose curve is defined by r=4sin⁡(3θ)r=4\sin(3\theta) for 0≤θ≤2π0\le\theta\le2\pi. (a) Determine the smallest positive interval of θ\theta for which the curve traces exactly one complete loop (petal), beginning and ending at the pole. (b) Compute the exact area enclosed by that single loop.

Related theory

Browse the problem library