9. Polar Equations

Convert x² + (y + 8)² = 64 to a polar equation that expresses r in terms of 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, 90°)

In Exercises 13–14, graph each polar equation.r = 1 + sin θ

In Exercises 13–34, 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 13–34, test for symmetry and then graph each polar equation.r = 2 + 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.(−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°)