Let describe a curve for .

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

Problem

Let

r=2+2\sin\theta

describe a curve for

0\le \theta\le 2\pi

. (1) Derive an explicit expression for

\dfrac{dy}{dx}

in terms of

\theta

. Your final answer should be fully simplified. (2) Evaluate the slope

\dfrac{dy}{dx}

\theta=\dfrac\pi6

and at

\theta=\dfrac{5\pi}6

. Provide exact values. (3) Interpret the meaning of the two slopes calculated in part (b) with respect to the graph of the curve in the

xy

–plane.