Differentiation in Polar Coordinates Lesson 10.7

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

3 Finding dy/dx We know  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

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

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