9. Polar Equations

Use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (3, 90°)

Graph each polar equation. r = 1 + sin θ

Test for symmetry and then graph each polar equation. r = 2 cos θ

In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (3, 4π/3)

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

In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (−1, π)

In Exercises 11–20, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. (−2, − π/2)

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 + cos θ

In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. Then find another representation of this point in which

a. r>0, 2π < θ < 4π.

b. r<0, 0. < θ < 2π.

c. r>0, −2π. < θ < 0.

(5, π/6)

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 1 + 2 cos θ

In Exercises 13–34, test for symmetry and then graph each polar equation. r = 2 − 3 sin θ

In Exercises 21–26, use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. Then find another representation of this point in which a. r>0, 2π < θ < 4π. b. r<0, 0. < θ < 2π. c. r>0, −2π. < θ < 0. (4, π/2)

In Exercises 27–32, select the representations that do not change the location of the given point. (7, 140°) (−7, 320°)

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