9. Polar Equations

Plot the point on the polar coordinate system.

$(-2,\(\frac{2\pi}{3}\))$

Plot the point $(3,\(\frac{\pi}{2}\))$ & find another set of coordinates, $(r,θ)$, for this point, where:

(A) $r≥0,2π≤θ≤4π$,

(B) $r≥0,-2π≤θ≤0$,

(C) $r≤0,0≤θ≤2π$.

Plot the point $(5,-\(\frac{\pi}{3}\))$, then identify which of the following sets of coordinates is the same point.

Plot the point $(-3,-\(\frac{\pi}{6}\))$, then identify which of the following sets of coordinates is the same point.

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, 225°)

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)

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)

Indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. (3, −135°)

Test for symmetry with respect to a. the polar axis. b. the line θ = π/2. c. the pole. r = 4 + 3 cos θ

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

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

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

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