Differentiation in Polar Coordinates Lesson 10.7

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

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

Finding dy/dx Since Then

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

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

Assignment Lesson 10.7 Page 443 Exercises 1 – 21 odd