1. Differentiation in Polar Coordinates
Lesson 10.7

2. Review Relationship of polar and rectangular systems
x = r cos θ y = r sin θ
Given r = f(θ), simple to find dr/dθ
However, we seek dy/dx

3. Finding dy/dx We know Then And
r = f(θ) and y = r sin θ and x = r cos θ
Then
And

4. Finding dy/dx
Since
Then

5. Example
Given r = cos 3θ
Find the slope of the line tangent at (1/2, π/9)
dy/dx = ?
Evaluate •

6. Define for Calculator
It is possible to define this derivative as a function on your calculator

7. Try This! Find where the tangent line is horizontal for r = 2 cos θ
Find dy/dx
Set equal to 0, solve for θ

8. Assignment
Lesson 10.7
Page 443
Exercises 1 – 21 odd