1. Polar Coordinates and Polar Graphs
Section 9.4 AP Calculus

2. Find the coordinate in rectangular and polar form.

3. Thm 9.10 Coordinate Conversion
The polar coordinates (r,θ) of a point are related to the rectangular coordinates (x,y) of the point as follows:
1) 2)

4. A) If (r,θ) = , find (x,y).
B) If (x,y) = (-2,-2), find (r,θ).

5. Graph:
A) r=4 B)
C) r=cscθ D) r=4cos5θ

6. Thm 9.11 Slope in Polar Form
If f is a differentiable function of θ, then the slope of the tangent line to the graph of r=f(θ) at point (r,θ) is

7. Horizontal Tangent:
Vertical Tangent:

8. Find and the slope of the tangent lines at (2,0) and

9. Find the Horizontal and Vertical Tangents of r=cosθ when 0≤θ≤π.

10. Thm 9.12 Tangent Lines at a Pole
If f(α)=0 and f’(α)≠0, then the line θ=α is tangent at the pole to the graph r=f(θ).

11. Look at when -π≤θ≤π.
Find where the graph has lines tangent to the pole.

12. Review of Polar Functions
Limaçon Circle
Rose Curve Lemniscate