9. Polar Equations

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?

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?

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

In the polar coordinate system, what is the name for a set of coordinates such as the one indicated with $c$ (for example, $(r,\theta )$)?

Plot the point on the polar coordinate system.

$(5,210°)$

Plot the point on the polar coordinate system.

$(-3,-90°)$

Plot the point on the polar coordinate system.

$(6,-\frac{11\pi}{6})$

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.