16. Parametric Equations & Polar Coordinates

40–41. {Use of Tech} Slopes of tangent lines

b. Find the slope of the lines tangent to the curve at the origin (when relevant).

r =3 − 6 cos θ

Find the slope of the tangent line of the polar curve $r=2\cos \theta$ at $\theta =\frac{\pi }{3}$.

Find the area enclosed by the cardioid $r=2-2\sin \theta$ between $\theta =\frac{\pi }{6}$ and $\theta =\frac{2\pi }{3}$.

11–20. Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points.

r = 1 - sin θ; (1/2, π/6)

11–20. Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points.

r = 4 + sin θ; (4, 0) and (3, 3π/2)

11–20. Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points.

r = 4 cos 2θ; at the tips of the leaves