16. Parametric Equations & Polar Coordinates

Given three polar coordinate representations for the origin.

57–64. Graphing polar curves Graph the following equations. Use a graphing utility to check your work and produce a final graph.

r² = 4 sin θ  

Convert the point to polar coordinates.

$(-2,2)$

Graph $r^2=9\(\sin\)2\(\theta\)$

Convert the point to rectangular coordinates.

$(-3,0)$

31–36. Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least two different ways.

(1, √3)

Polar Coordinates

Plot the following points, given in polar coordinates. Then find all the polar coordinates of each point.

a. (2, π/2)

25–30. Converting coordinates Express the following polar coordinates in Cartesian coordinates.

(2, 7π/4)

What is the polar equation of a circle of radius √(a²+b²) centered at (a, b)?

27–32. Polar curves Graph the following equations.

r = 3 cos 3θ

15–22. Sets in polar coordinates Sketch the following sets of points.

2 ≤ r ≤ 8

53–56. Simple curves Tabulate and plot enough points to sketch a graph of the following equations.

r = 1 - cos θ

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

Convert the point to rectangular coordinates.

$(0,\(\frac{7\pi}{4}\))$

Convert each equation to its polar form.

$y-x=6$