积极 AI Logo 积极 AI

正弦函数的直观导数

正弦函数的直观导数
几何画板及绘图内容加载中，请稍等……
2018-07-05 06:55
函数三角函数导数
这个范例演示了正弦函数的直观导数。它涉及三角函数和导数的核心数学概念。通过构造摘要中的命令，如Point, Segment, Rotate, Slope等，可以清晰地看到正弦函数在不同点的导数值。适合高中数学教学和学习使用。

GeoGebra 命令及参数

  1. Point(f) → E
  2. Point(f) → F
  3. Point(f) → G
  4. Point(f) → H
  5. Segment((x(A) - d, y(A)), (x(A) + d, y(A))) → A_s
  6. Rotate(A_s, atand(m_1), A) → A_s'
  7. Slope(A_s') → m
  8. Segment((x(B) - d, y(B)), (x(B) + d, y(B))) → B_s
  9. Rotate(B_s, atand(m_2), B) → B_s'
  10. Point(A_s') → I
  11. OrthogonalLine(I, xAxis) → i
  12. Point(A_s') → J
  13. OrthogonalLine(J, xAxis) → j
  14. OrthogonalLine(J, j) → k
  15. Intersect(i, k) → K
  16. Vector(I, K) → u
  17. Vector(K, J) → w
  18. Dilate(w, If[1 < a ≤ 2, a - 1, 0]) → v1_x
  19. Dilate(u, If[0 ≤ a ≤ 1, a, 1]) → v1_y
  20. Segment((x(C) - d, y(C)), (x(C) + d, y(C))) → C_s
  21. Segment((x(D) - d, y(D)), (x(D) + d, y(D))) → D_s
  22. Rotate(C_s, atand(m_3), C) → C_s'
  23. Rotate(D_s, atand(m_4), D) → D_s'
  24. Pendiente2(B, m_2, d, a) → v2_y, v2_x
  25. Pendiente2(C, m_3, d, a) → v3_y, v3_x
  26. Pendiente2(D, m_4, d, a) → v4_y, v4_x
  27. Segment(A, A_m) → l
  28. Segment(B, B_m) → n
  29. Segment(C, C_m) → q
  30. Segment(D, D_m) → r
  31. Vector(A_0, A_m) → showAN
  32. Vector(A_0, A_m) → showAP
  33. Derivative(f) → f'
  34. Vector(B_0, B_m) → showBP
  35. Vector(B_0, B_m) → showBN
  36. Vector(C_0, C_m) → showCN
  37. Vector(C_0, C_m) → showCP
  38. Vector(D_0, D_m) → showDN
  39. Vector(D_0, D_m) → showDP
  40. Segment((x(E) - d, y(E)), (x(E) + d, y(E))) → E_s
  41. Segment((x(F) - d, y(F)), (x(F) + d, y(F))) → F_s
  42. Segment((x(G) - d, y(G)), (x(G) + d, y(G))) → G_s
  43. Segment((x(H) - d, y(H)), (x(H) + d, y(H))) → H_s
  44. Rotate(E_s, atand(m_5), E) → E_s'
  45. Rotate(F_s, atand(m_6), F) → F_s'
  46. Rotate(G_s, atand(m_7), G) → G_s'
  47. Rotate(H_s, atand(m_8), H) → H_s'
  48. Vector(E_0, E_m) → showEP
  49. Vector(E_0, E_m) → showEN
  50. Vector(F_0, F_m) → showFN
  51. Vector(G_0, G_m) → showGN
  52. Vector(G_0, G_m) → showGP
  53. Vector(H_0, H_m) → showHP
  54. Vector(H_0, H_m) → showHN
  55. Vector(F_0, F_m) → showFP