1. CH 11 PARAMETRIC EQUATIONS AND POLAR COORDINATES 參數方程式與極座標

2. 學習內容 參數曲線 • 11.2 Parametric Curves • 11.3 Polar Coordinates 極座標

3. 11.2 Parametric Curves 參數曲線

4. 學習重點 • 知道函數的極座標表示法 • 會求極座標之曲線的切線斜率

5. 直角座標與極座標

6. P點的直角座標與P點的極座標 • P點的直角座標 = (x, y) • P點的極座標 = (r, θ) ‧

7. 極座標曲線之導函數 • a polar curve r = f (θ) x =r cosθ = f (θ) cosθ y =r sinθ = f (θ) sinθ

8. Example 9 (a) For the cardioid r =f (θ) = 1 + sinθ, find the slope of the tangent line whenθ = π/3.

9. θ=π/3 θ θ θ θ

10. Example 9 (b) Find the points on the cardioid where the tangent line is horizontal or vertical. Horizontal tangent Vertical tangent

11. horizontal tangents at the points • (2, π/2), (½, 7π/6), (½, 11π/6) • vertical tangents at at the points • (3/2, π/6), (3/2, 5π/6)

12. Q1 Find the slope of the tangent line to the curve r=1/θ at θ=π. (a) (b) (c) (d)