91Ó°ÊÓ

Graph the curve and find the area that it encloses. $$r=3-2 \cos 4 \theta$$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$ x=t^{3}-3 t, \quad y=t^{3}-3 t^{2} $$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$x=2 \cos \theta, \quad y=\sin 2 \theta$$

Identify the curve by finding a Cartesian equation for the curve. $$r^{2} \cos 2 \theta=1$$

\(15-18=\) Describe the motion of a particle with position \((x, y)\) as \(t\) varies in the given interval. $$x=3+2 \cos t, \quad y=1+2 \sin t, \quad \pi / 2 \leqslant t \leqslant 3 \pi / 2$$

Find the area of the region enclosed by one loop of the curve. $$r=4 \cos 3 \theta$$

\(9-16=(\) a) Find the eccentricity, (b) identify the conic, (c) give an equation of the directrix, and (d) sketch the conic. $$ r=\frac{3}{4-8 \cos \theta} $$

Find the area of the region enclosed by one loop of the curve. $$r^{2}=\sin 2 \theta$$

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. $$x=e^{\sin \theta}, \quad y=e^{\cos \theta}$$

\(15-18=\) Describe the motion of a particle with position \((x, y)\) as \(t\) varies in the given interval. $$x=2 \sin t, \quad y=4+\cos t, \quad 0 \leqslant t \leqslant 3 \pi / 2$$