9. Polar Equations

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 4 sin 3θ

Indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (−3, −3π/4)

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (−4, π/2)

Given the point with polar coordinates $(3,\frac{\pi }{4})$, which of the following polar coordinate pairs labels the same point?

Given the point with polar coordinates $(3,\frac{\pi }{4})$, which of the following polar coordinate pairs represents the same point?

In Exercises 27–32, select the representations that do not change the location of the given point. (4, 120°) (−4, 300°)

Use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (2, 45°)

Find two different sets of parametric equations for y = x² + 6.

In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, π)

In Exercises 1–10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (−3, 5π/4)

Eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. x = √t , y = t + 1; −∞ < t < ∞

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 − 3 sin θ

Plot the point on the polar coordinate system.

$(-3,-90°)$

Which of the following correctly expresses the conversion from rectangular coordinates $(x,y,z)$ to cylindrical coordinates $(r,\theta ,z)$?