9. Polar Equations

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

$r=4\sin2\theta$

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

$r=3+2\cos\theta$

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

$r^2=-25\cos2\theta$

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

$r=1-\sin\theta$

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

r = cos 3θ

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

r = cos 2θ

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

r = 2/(cosθ + sinθ)

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

r = 2 + 2 cos θ