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单位圆上的三角函数 by Sete Cordas

单位圆上的三角函数 by Sete Cordas
几何画板及绘图内容加载中，请稍等……
2017-10-03 23:13
圆向量函数三角函数几何作图
本范例演示单位圆上的三角函数关系。核心数学概念包括三角函数、单位圆和向量。通过使用GeoGebra命令如Intersect、Circle、Point等，可以动态展示正弦、余弦、正切等函数的图像。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A_2
  2. Circle(A_2, 1) → c
  3. Point(c) → A
  4. Segment(A_2, A) → r
  5. Line(A, xAxis) → g
  6. OrthogonalLine(A, xAxis) → h
  7. Intersect(h, xAxis) → C
  8. Segment(A_2, C) → i
  9. Segment(C, A) → rsinθ
  10. OrthogonalLine(A, r) → l
  11. Intersect(l, yAxis) → D
  12. Intersect(l, xAxis) → E
  13. Segment(A_2, E) → m
  14. Segment(A_2, D) → n
  15. Segment(E, D) → p
  16. Angle(C, A_2, A) → θ
  17. OrthogonalLine(A, n) → q
  18. Segment(A, E) → rtanθ
  19. Segment(A, D) → rcotanθ
  20. Intersect(q, n) → F
  21. Segment(A, F) → rcosθ
  22. PointIn(c) → Pointc
  23. Intersect(rsinθ, m) → G
  24. Intersect(c, m, 1) → H
  25. Segment(G, H) → rversinθ
  26. Segment(H, E) → rexsecθ
  27. Intersect(c, n, 1) → I
  28. Segment(I, D) → rexcscθ
  29. Segment(I, F) → rcoversθ
  30. OrthogonalLine(E, g) → f
  31. Point(f) → J
  32. OrthogonalLine(J, f) → j
  33. Intersect(j, yAxis) → K
  34. Segment(J, K) → rsecθ
  35. Vector(K, J) → u
  36. Vector(J, K) → v
  37. Line(D, xAxis) → k
  38. Point(k) → L
  39. OrthogonalLine(L, k) → n_1
  40. Intersect(n_1, xAxis) → M
  41. Vector(L, M) → w
  42. Vector(M, L) → a
  43. Segment(L, M) → rcscθ
  44. Intersect(rcosθ, rcoversθ) → N
  45. Intersect(r, i) → O
  46. Segment(O, N) → s
  47. OrthogonalLine(P, rcosθ) → t
  48. OrthogonalLine(Q, yAxis) → b
  49. Segment(F, Q) → rcovercosθ
  50. Point(b) → R
  51. OrthogonalLine(R, rcosθ) → d
  52. Intersect(g, d) → S
  53. Vector(R, S) → e
  54. Vector(S, R) → u_1
  55. Intersect(c, xAxis, 1) → T
  56. OrthogonalLine(T, xAxis) → f_1
  57. Point(f_1) → U
  58. Line(U, xAxis) → g_1
  59. Intersect(h, g_1) → V
  60. Vector(U, V) → v_1
  61. Vector(V, U) → w_1
  62. Segment(U, V) → rvercosθ
  63. Intersect(r, i) → Z
  64. Intersect(i, rsinθ) → A_1
  65. Intersect(rtanθ, xAxis) → B_1
  66. Line(B_1, yAxis) → h_1
  67. Point(h_1) → C_1
  68. Angle(C_1, B_1, A) → α
  69. Angle(A, B_1, A_1) → δ
  70. Point(rcosθ) → W
  71. Angle(F, A, A_2) → γ
  72. Angle(D, A, F) → ζ
  73. Angle(A_2, A, C) → β
  74. Angle(C, A, E) → ε
  75. Angle(I, D, A) → ι
  76. Angle(r, s) → η