积极 AI Logo 积极 AI

正弦、余弦和正切函数演示

正弦、余弦和正切函数演示
几何画板及绘图内容加载中，请稍等……
2016-06-11 02:41
向量三角函数解析几何几何作图函数图像
①本范例通过动态演示直角三角形中的正弦、余弦和正切函数关系，直观展示三角函数的定义和几何意义；②涉及的核心数学概念包括三角函数、直角三角形、单位圆、向量、坐标几何；③作图要点提炼自GeoGebra命令：Intersect（交点）、Circle（圆）、Point（点）、Rotate（旋转）、Vector（向量）、Midpoint（中点）、Segment（线段）、CurveCartesian（笛卡尔曲线）、Polygon（多边形）、OrthogonalLine（垂线）、If（条件语句）；④适合高中数学学生学习和理解三角函数的几何基础，也可用于大学基础数学教学。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 3) → c
  3. Point(c) → B
  4. Rotate(B, β, A) → B'_1
  5. Vector(A, B'_1) → v
  6. Point(v) → E
  7. Midpoint(I, F) → J
  8. Midpoint(F, J) → K
  9. Midpoint(J, I) → L
  10. Midpoint(B, G) → M
  11. Midpoint(B, H) → N
  12. Segment(J, B) → k
  13. Segment(K, M) → l
  14. Midpoint(I, H) → O
  15. Midpoint(I, O) → P
  16. Midpoint(O, H) → Q
  17. Midpoint(F, G) → R
  18. Midpoint(F, R) → S
  19. Midpoint(R, G) → T
  20. Segment(P, S) → m
  21. Segment(Q, T) → p
  22. Point(g) → U
  23. Point(g) → V
  24. Point(g) → W
  25. Point(g) → Z
  26. Segment(R, O) → a_1
  27. CurveCartesian(((a * α) * cos(α)), ((a * α) * sin(α)), α, 0, β) → d
  28. CurveCartesian(((a * α) * cos(α)), (((-a) * α) * sin(α)), α, 0, (-β)) → e
  29. Segment(L, N) → t
  30. Vector(C_3, C_2) → u
  31. Vector(C_4, C_1) → w
  32. Point(g) → C
  33. Point(g) → D
  34. Point(g) → A_1
  35. Point(g) → B_1
  36. Point(g) → D_1
  37. Point(g) → E_1
  38. Point(j) → F_1
  39. Point(g) → G_1
  40. Point(g) → H_1
  41. Point(g) → I_1
  42. Point(g) → J_1
  43. Point(g) → K_1
  44. Intersect(g, yAxis, (0, -6)) → L_1
  45. Vector(C_6, C_5) → u_1
  46. Polygon(M_1, N_1, O_1, P_1) → poly2, m_1, n_1, o_1, p_3
  47. Vector(J_1, W_1) → v_1
  48. Vector(J_1, Z_1) → w_1
  49. Point(yAxis) → A_2
  50. Vector(J_1, A_2) → c_1
  51. Point(xAxis) → B_2
  52. Point(xAxis) → D_2
  53. Vector(B_2, D_2) → d_1
  54. Point(yAxis) → E_2
  55. Vector(A_2, E_2) → e_1
  56. OrthogonalLine(B'_1, xAxis) → i_1
  57. Intersect(i_1, xAxis) → F_2
  58. Vector(F_2, B'_1) → j_1
  59. Segment(B'_1, F_2) → k_1
  60. Point(e_1) → G_2
  61. Midpoint(F_2, B'_1) → H_2
  62. Segment(G_2, F_2) → l_1
  63. Midpoint(G_2, F_2) → I_2
  64. OrthogonalLine(B'_1, a_1) → a_2
  65. Intersect(a_1, yAxis) → J_2
  66. Intersect(a_2, yAxis) → K_2
  67. Vector(G_2, F_2) → u_2
  68. Polygon(L_2, M_2, N_2, O_2) → poly1, l_2, m_2, n_2, o_2
  69. Segment(A, B'_1) → b
  70. Midpoint(A, B'_1) → P_2
  71. Point(b) → Q_2
  72. Polygon(R_2, S_2, T_2, U_2) → poly3, r_2, s_2, t_2, u_3
  73. If(1000 < yxtan < -1000, text45) → text46
  74. Point(c_1) → V_2
  75. Point(c) → W_2
  76. Point(c) → Z_2
  77. Point(c) → A_3
  78. Point(c) → B_3
  79. Point(c) → D_3
  80. Point(c) → E_3
  81. Point(c) → F_3
  82. Point(c) → G_3
  83. Point(c) → H_3
  84. Point(c) → I_3
  85. Point(c) → J_3
  86. Point(c) → K_3
  87. Point(c) → L_3
  88. Point(c) → M_3
  89. Point(c) → N_3
  90. Point(c) → O_3