Consider the polar curve given by for .

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider the polar curve given by

r = 2 + 2\sin\theta

for

0 \le \theta \le 2\pi

. (1) Part 1: (a) Determine the Cartesian coordinates

(x,y)

of the point on the curve that corresponds to

\theta=\dfrac{\pi}{6}

. (2) Part 2: (b) Calculate

\dfrac{dy}{dx}

\theta=\dfrac{\pi}{6}

. (3) Part 3: (c) Write the equation of the tangent line at that point in point–slope form and then rewrite it in slope–intercept form.