9. Polar Equations

Graph $r=2-2\(\cos\]\theta\)$

In Exercises 35–44, test for symmetry and then graph each polar equation. r = 1 / 1−cos θ

Which of the following best describes the graph of the polar equation $r=2-2\cdot \sin \left(\theta \right)$?

Graph $r=3\(\cos\)4\(\theta\)$

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.

$r=4\(\sin\)2\(\theta\)$

Given the limaçon $r=1+2\cos \left(\theta \right)$, find the area that lies inside the larger loop and outside the smaller loop.

Which of the following best describes the graph of the polar equation $r=1+\cos (25\theta )$?

Match each equation with its polar graph from choices A–D.

r = cos 3θ

Graph $r=1+2\(\sin\]\theta\)$

Graph each polar equation. Also, identify the type of polar graph.

r = 2 + 2 cos θ

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.

$r=1-\(\sin\]\theta\)$

Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.

$r^2=-25\(\cos\)2\(\theta\)$

Which of the following best describes the graph of the polar curve $r=4\cos \left(3\theta \right)$?

Match each equation with its polar graph from choices A–D.

r = cos 2θ

In Exercises 64–70, graph each polar equation. Be sure to test for symmetry. r = 2 + 2 sin θ