9. Polar Equations

Given the polar equation $r=9\cos \left(\theta \right)$, which of the following is its equivalent Cartesian equation?

Which of the following best describes the graph of the polar curve $r=2+5\sin \left(\theta \right)$?

Find the exact length of the polar curve $r=2$ for $0\le \theta \le 2\pi$.

The graph of the polar curve $r=\pi$ is shown above for $0\le \theta \le 3\pi$. What is the area of the shaded region?

Given the polar equation $r=5\cos \left(\theta \right)$, which of the following is its Cartesian equation?

What are the rectangular coordinates of the point whose cylindrical coordinates are $3,120°,5$?

Given the polar equation $r=6$, which of the following is the corresponding Cartesian equation?

Plot the point on the polar coordinate system.

$(5,210°)$

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

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

In Exercises 59–74, convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation.

r = 6 cos θ + 4 sin θ

In Exercises 71–76, eliminate the parameter and graph the plane curve represented by the parametric equations. Use arrows to show the orientation of each plane curve. x = 2t − 1, y = 1 − t; −∞ < t < ∞

In Exercises 35–44, test for symmetry and then graph each polar equation. r = cos θ/2

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (4, 90°)

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°)