9. Polar Equations

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

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

$r=4\sin2\theta$

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 $r=1+\cos (25\theta )$?

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

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.

$r=1-\sin\theta$

Graph $r=2-2\cos\theta$

Graph $r=1+2\sin\theta$

Graph $r=3\cos4\theta$

Graph $r^2=9\sin2\theta$

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)