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坐标系中的函数与几何

坐标系中的函数与几何
几何画板及绘图内容加载中，请稍等……
2015-08-05 03:43
函数三角函数解析几何
本范例通过输入函数并利用几何图形来抽象函数信息，涉及三角函数、向量和解析几何等核心概念。使用了半圆、线段、圆、多边形、向量、角度、点、距离、交点、镜像、文本框、斜率、旋转等GeoGebra命令。适合高中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Semicircle(C, D) → c
  2. Semicircle(D, C) → d
  3. Segment(A, D) → a
  4. Circle(A, 1) → f
  5. Semicircle(E, F) → r
  6. Semicircle(F, E) → g
  7. Polygon(B, A, C, G) → poly1, b_1, a_1, c_1, g_1
  8. Vector((1.414213562373095, 1.414213562373095)) → u_3
  9. Vector((1.79, 0.89)) → v
  10. Segment(G, B) → ζ_1
  11. Segment(G, J) → h
  12. Segment(G, K) → i
  13. Angle(B, G, K) → α_u
  14. Angle(B, G, J) → β_v
  15. Vector((0.89, 1.79)) → w
  16. Segment(G, L) → j
  17. Angle(B, G, L) → δ_w
  18. Angle(J, G, L) → Δ_v
  19. Circle(G, K) → k
  20. Point(r) → N
  21. Point(g) → M
  22. Segment(N, A) → p
  23. Segment(A, M) → q
  24. Segment(M, N) → s
  25. Polygon(N, C, G, B, M) → poly2, n_1, c_2, g_2, b_2, m_1
  26. Vector((2, 1)) → t
  27. Vector((1, 2)) → u
  28. Segment(G, N) → d_1
  29. Segment(G, M) → e_1
  30. Angle(M, G, N) → α_t
  31. Segment(A, R) → k_1
  32. Segment(A, Q) → l_1
  33. Segment(Q, R) → p_1
  34. Circle(A, S) → q_1
  35. Distance(G, A) → distanceGA
  36. Point(Circle[A, 3]) → T
  37. Segment(A, T) → r_1
  38. Point(Circle[G, 3]) → U
  39. Segment(G, U) → s_1
  40. Point(Circle[T, 2.8284271247461903]) → V
  41. Segment(T, V) → t_1
  42. Distance(G, Q) → distanceGQ
  43. Distance(G, M) → distanceGM
  44. Segment(G, M) → a_2
  45. Segment(W, Z) → d_2
  46. Vector(A_1, B_1) → u_2
  47. Vector(C_1, D_1) → v_2
  48. Distance(G, N) → distanceGN
  49. Segment(G, N) → f_2
  50. Distance(G, Q) → j_2
  51. Point(k) → E_1
  52. Point(k) → F_1
  53. Distance(F_1, E_1) → distanceF1E1
  54. Segment(E_1, F_1) → k_2
  55. Point(k_2) → G_1
  56. Point(s) → H_1
  57. Distance(G_1, H_1) → distanceG1H1
  58. Segment(G_1, H_1) → l_2
  59. Segment(I_1, J_1) → m_2
  60. Segment(K_1, L_1) → n_2
  61. Segment(K_2, L_2) → n_3
  62. Segment(K_3, L_3) → n_4
  63. Segment(K_4, L_4) → n_5
  64. Segment(K_5, L_5) → n_6
  65. Segment(K_8, L_8) → n_9
  66. Polygon(M_1, N_1, O_1, P_1) → poly3, m_3, n_{13}, o_2, p_2
  67. Intersect(k, q_1, 1) → Q_1
  68. Point(f_2) → R_1
  69. Circle(Q_1, R_1) → q_2
  70. Mirror(q_2, i) → r_2
  71. Segment(S_1, T_1) → a_3
  72. Segment(U_1, V_1) → b_3
  73. Intersect(f_3, i, 1) → W_1
  74. Point(f_3) → Z_1
  75. Segment(W_1, Z_1) → d_3
  76. Textfield(σ) → inputBox1
  77. Point(f_3) → C_2
  78. Point(f_3) → D_2
  79. Vector(G, D_2) → v_3
  80. Distance(G, D_2) → distanceGD2
  81. Vector(E_2, F_2) → w_3
  82. Mirror(N, p_1) → N'
  83. Mirror(A, p_1) → A'
  84. Segment(N', A') → p'
  85. Mirror(A, p_1) → A'_1
  86. Mirror(R, p_1) → R'
  87. Segment(A'_1, R') → g_3
  88. Mirror(A, p_1) → A'_2
  89. Mirror(M, p_1) → M'
  90. Segment(A'_2, M') → q'
  91. Mirror(A, p_1) → A'_3
  92. Mirror(Q, p_1) → Q'
  93. Segment(A'_3, Q') → h_3
  94. Segment(G, D_2) → i_3
  95. Slope(i_3) → m_4
  96. Point(p_3) → G_2
  97. Distance(G, G_2) → distanceGG2
  98. Vector(G, G_2) → j_3
  99. Segment(G, G_2) → l_3
  100. Angle(K, G, G_2) → α
  101. Point(q_3) → H_2
  102. Point(s_3) → I_2
  103. Point(r_3) → J_2
  104. Polygon(H_2, I_2, J_2, G) → poly4, h_4, i_4, j_4, g_4
  105. Point(h_4) → M_2
  106. Point(j_4) → N_2
  107. Point(i_4) → O_2
  108. Point(g_4) → P_2
  109. Segment(O_2, M_2) → t_3
  110. Segment(N_2, P_2) → a_4
  111. Point(a_4) → Q_2
  112. Point(t_3) → R_2
  113. Segment(Q_2, R_2) → b_4
  114. Point(i_4) → T_2
  115. Point(f_4) → U_2
  116. Point(e_4) → S_2
  117. Segment(S_2, U_2) → k_4
  118. Point(p_4) → V_2
  119. Segment(G, V_2) → l_4
  120. Point(q_4) → W_2
  121. Point(κ) → Z_2
  122. Segment(G, W_2) → λ
  123. Segment(G, Z_2) → r_4
  124. Angle(Z_2, G, W_2) → β
  125. Vector(G, W_2) → ζ
  126. Point(κ) → A_3
  127. Point(κ) → B_3
  128. Segment(A_3, B_3) → e
  129. Point(e) → D_3
  130. Textfield(μ) → inputBox2
  131. Rotate(A_3, 90*°, G) → E_3
  132. Rotate(B_3, 90*°, G) → F_3
  133. Segment(E_3, F_3) → e'
  134. Point(e) → C_3
  135. Rotate(A_3, 90*°, C_3) → G_3
  136. Rotate(B_3, 90*°, C_3) → H_3
  137. Segment(G_3, H_3) → e'_1
  138. Mirror(E_3, e'_1) → I_3
  139. Mirror(F_3, e'_1) → J_3
  140. Segment(I_3, J_3) → e''
  141. Point(e'') → M_3
  142. Point(e'') → N_3
  143. Segment(G, N_3) → s_4