The curve is traced once as increases from to .

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

Problem

The curve

r=2\sin\theta

is traced once as

\theta

increases from

0

\pi

. (a) Show that the curve passes through the origin when

\theta=0

and

\theta=\pi

. (b) Determine

\dfrac{dy}{dx}

for the curve and identify every value of

\theta

(0,\pi)

where

\dfrac{dy}{dx}=0

. (c) For each

\theta

found in part (b), compute

\dfrac{d^2y}{dx^2}

and decide whether the corresponding point on the curve is a local point of inflection. Justify your answer.