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利用三角函数求角度

利用三角函数求角度
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2017-06-20 07:09
角三角函数
本范例通过三角函数求解角度。演示了如何利用三角函数知识求解角度，涉及的核心数学概念包括三角函数、角度计算等。使用了GeoGebra中的Random, Line, OrthogonalLine, Segment, Intersect, Polygon, Angle, Midpoint, Length, If等命令。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Random(1, 4) → randn
  2. Line(A, B) → f
  3. OrthogonalLine(C, f) → g
  4. Segment(C, B) → h
  5. Intersect(f, g) → D
  6. Polygon(C, D, B) → poly1, b, c, d
  7. Angle(D, C, B) → α
  8. Angle(C, B, D) → β
  9. Angle(B, D, C) → γ
  10. Random(1, 6) → questionrand
  11. Midpoint(C, B) → E
  12. Midpoint(B, D) → F
  13. Midpoint(D, C) → G
  14. Length(Segment[C, D]) → Segb
  15. Length(Segment[D, B]) → Segc
  16. Length(Segment[B, C]) → Segd
  17. Line(A_1, B_1) → f_1
  18. OrthogonalLine(C_1, f_1) → g_1
  19. Segment(C_1, B_1) → h_1
  20. Intersect(f_1, g_1) → D_1
  21. Polygon(C_1, D_1, B_1) → poly1_1, b_1, c_1, d_1
  22. Angle(D_1, C_1, B_1) → α_1
  23. Angle(C_1, B_1, D_1) → β_1
  24. Angle(B_1, D_1, C_1) → γ_1
  25. Midpoint(C_1, B_1) → E_1
  26. Midpoint(B_1, D_1) → F_1
  27. Midpoint(D_1, C_1) → G_1
  28. Line(A_2, B_2) → f_2
  29. OrthogonalLine(C_2, f_2) → g_2
  30. Segment(C_2, B_2) → h_2
  31. Intersect(f_2, g_2) → D_2
  32. Polygon(C_2, D_2, B_2) → poly1_2, b_2, c_2, d_2
  33. Angle(D_2, C_2, B_2) → α_2
  34. Angle(C_2, B_2, D_2) → β_2
  35. Angle(B_2, D_2, C_2) → γ_2
  36. Midpoint(C_2, B_2) → E_2
  37. Midpoint(B_2, D_2) → F_2
  38. Midpoint(D_2, C_2) → G_2
  39. If(j ≟ 1 ∨ j ≟ 2, "CAH", If[j ≟ 3 ∨ j ≟ 4, "SOH", If[j ≟ 5 ∨ j ≟ 6, "TOA", "ANSWERS"]]) → captionSlider
  40. Line(A_5, B_5) → f_5
  41. OrthogonalLine(C_5, f_5) → g_5
  42. Segment(C_5, B_5) → h_3
  43. Intersect(f_5, g_5) → D_5
  44. Polygon(C_5, D_5, B_5) → poly1_4, b_4, c_4, d_4
  45. Angle(D_5, C_5, B_5) → α_3
  46. Angle(C_5, B_5, D_5) → β_4
  47. Angle(B_5, D_5, C_5) → γ_3
  48. Midpoint(C_5, B_5) → E_3
  49. Midpoint(B_5, D_5) → F_3
  50. Midpoint(D_5, C_5) → G_3
  51. Line(A_4, B_4) → f_4
  52. OrthogonalLine(C_4, f_4) → g_4
  53. Segment(C_4, B_4) → h_4
  54. Intersect(f_4, g_4) → D_4
  55. Polygon(C_4, D_4, B_4) → poly1_5, b_5, c_5, d_5
  56. Angle(D_4, C_4, B_4) → α_4
  57. Angle(C_4, B_4, D_4) → β_3
  58. Angle(B_4, D_4, C_4) → γ_4
  59. Midpoint(C_4, B_4) → E_4
  60. Midpoint(B_4, D_4) → F_4
  61. Midpoint(D_4, C_4) → G_4
  62. Line(A_8, B_8) → f_8
  63. OrthogonalLine(C_8, f_8) → g_8
  64. Segment(C_8, B_8) → h_6
  65. Intersect(f_8, g_8) → D_8
  66. Polygon(C_8, D_8, B_8) → poly1_7, b_7, c_7, d_7
  67. Angle(D_8, C_8, B_8) → α_6
  68. Angle(C_8, B_8, D_8) → β_7
  69. Angle(B_8, D_8, C_8) → γ_6
  70. Midpoint(C_8, B_8) → E_6
  71. Midpoint(B_8, D_8) → F_6
  72. Midpoint(D_8, C_8) → G_6
  73. Line(A_7, B_7) → f_7
  74. OrthogonalLine(C_7, f_7) → g_7
  75. Segment(C_7, B_7) → h_7
  76. Intersect(f_7, g_7) → D_7
  77. Polygon(C_7, D_7, B_7) → poly1_8, b_8, c_8, d_8
  78. Angle(D_7, C_7, B_7) → α_7
  79. Angle(C_7, B_7, D_7) → β_6
  80. Angle(B_7, D_7, C_7) → γ_7
  81. Midpoint(C_7, B_7) → E_7
  82. Midpoint(B_7, D_7) → F_7
  83. Midpoint(D_7, C_7) → G_7
  84. Line(A_{11}, B_{11}) → f_{11}
  85. OrthogonalLine(C_{11}, f_{11}) → g_{11}
  86. Segment(C_{11}, B_{11}) → h_9
  87. Intersect(f_{11}, g_{11}) → D_{11}
  88. Polygon(C_{11}, D_{11}, B_{11}) → poly1_{10}, b_{10}, c_{10}, d_{10}
  89. Angle(D_{11}, C_{11}, B_{11}) → α_9
  90. Angle(C_{11}, B_{11}, D_{11}) → β_{10}
  91. Angle(B_{11}, D_{11}, C_{11}) → γ_9
  92. Midpoint(C_{11}, B_{11}) → E_9
  93. Midpoint(B_{11}, D_{11}) → F_9
  94. Midpoint(D_{11}, C_{11}) → G_9
  95. Line(A_{10}, B_{10}) → f_{10}
  96. OrthogonalLine(C_{10}, f_{10}) → g_{10}
  97. Segment(C_{10}, B_{10}) → h_{10}
  98. Intersect(f_{10}, g_{10}) → D_{10}
  99. Polygon(C_{10}, D_{10}, B_{10}) → poly1_{11}, b_{11}, c_{11}, d_{11}
  100. Angle(D_{10}, C_{10}, B_{10}) → α_{10}
  101. Angle(C_{10}, B_{10}, D_{10}) → β_9
  102. Angle(B_{10}, D_{10}, C_{10}) → γ_{10}
  103. Midpoint(C_{10}, B_{10}) → E_{10}
  104. Midpoint(B_{10}, D_{10}) → F_{10}
  105. Midpoint(D_{10}, C_{10}) → G_{10}