91Ó°ÊÓ

On a graphing utility, graph and sketch \(r=\sin \theta+\left(\sin \left(\frac{5}{2} \theta\right)\right)^{3}\) on \([0,4 \pi]\)

On a graphing utility, graph each polar equation. Explain the similarities and difference in the graphs. $$ \begin{array}{l}{r_{1}=3 \sin (3 \theta)} \\ {r_{2}=2 \sin (3 \theta)} \\\ {r_{3}=\sin (3 \theta)}\end{array} $$

On a graphing utility, graph each polar equation. Explain the similarities and differences you observe in the graphs. $$ \begin{array}{l}{r_{1}=3+3 \cos \theta} \\ {r_{2}=2+2 \cos \theta} \\\ {r_{3}=1+\cos \theta}\end{array} $$

On a graphing utility, graph each polar equation. Explain the similarities and differences you observe in the graphs. $$ \begin{array}{l}{r_{1}=3 \theta} \\ {r_{2}=2 \theta} \\\ {r_{3}=\theta}\end{array} $$

For the following exercises, draw each polar equation on the same set of polar axes, and find the points of intersection. $$ r_{1}=3+2 \sin \theta, \quad r_{2}=2 $$

For the following exercises, draw each polar equation on the same set of polar axes, and find the points of intersection. $$ r_{1}=6-4 \cos \theta, \quad r_{2}=4 $$

For the following exercises, draw each polar equation on the same set of polar axes, and find the points of intersection. $$ r_{1}=1+\sin \theta, \quad r_{2}=3 \sin \theta $$

For the following exercises, draw each polar equation on the same set of polar axes, and find the points of intersection. $$ r_{1}=1+\cos \theta, \quad r_{2}=3 \cos \theta $$

For the following exercises, draw each polar equation on the same set of polar axes, and find the points of intersection. $$ r_{1}=\cos (2 \theta), r_{2}=\sin (2 \theta) $$

For the following exercises, draw each polar equation on the same set of polar axes, and find the points of intersection. $$ r_{1}=\sin ^{2}(2 \theta), r_{2}=1-\cos (4 \theta) $$