1. Polar Coordinates
Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle)
Polar coordinates find the same point in a different way
r = distance from the origin (radius)
θ = angle with positive x-axis

2. Ex. The Cartesian coordinates of a point are given, find the polar coordinates.
(0,1)

3. Polar  Rect
Rect  Polar
Ex. The polar coordinates of a point are given, find the Cartesian coordinates.
(2,π)

4. Ex. Find the polar equation for the curve.
x2 + y2 = 3y
x3y2 + ln y = 3

5. Ex. Find the Cartesian equation for the curve.
r = cos θ
sin θ = r2 cos θ

6. Ex. Sketch the polar equation r = 3

7. Ex. Sketch the polar equation θ =

8. Ex. Sketch the polar equation r = sec θ.

9. Ex. Sketch the polar equation r = 2cos5θ

10. For the function r = f (θ),
Ex. Find the points of horizontal and vertical tangency on the graph r = sin θ, 0 ≤ θ ≤ 2.

11. Pract.
1. Convert the polar point to Cartesian.
2. Sketch the curve r = 2cos θ.
3. Find the slope of the tangent line to r = 1 + sin θ when θ =