16. Parametric Equations & Polar Coordinates

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.

$r=1-\sin\theta$

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

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

Graph $r=3\cos4\theta$

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

What is the slope of the line θ=π/3?

Without calculating derivatives, determine the slopes of each of the lines tangent to the curve r=8 cos θ−4 at the origin.

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

(x - 1)² + y² = 1

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

y = 3

49–52. Cartesian-to-polar coordinates Convert the following equations to polar coordinates.

y = x²

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r = 6 cos θ + 8 sin θ

37–48. Polar-to-Cartesian coordinates Convert the following equations to Cartesian coordinates. Describe the resulting curve.

r = 3 csc θ