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Graphing Trigonometric Functions

Graphing Trigonometric Functions
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2015-06-15 08:42
FunctionTrigonometryCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates how to graph trigonometric functions using GeoGebra. It involves core math concepts like trigonometric functions, function graphs, and analytical geometry. Key GeoGebra commands and objects used include Intersect, Point, Circle, Segment, Angle, OrthogonalLine, CircleArc, Function, Line, Polygon, and Mirror. It is suitable for high school students learning to plot trigonometric function graphs and understand their geometric properties and transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → b
  6. Angle(B, A, C) → θ
  7. Intersect(c, xAxis, 2) → E
  8. Segment(E, B) → a
  9. OrthogonalLine(C, a) → d
  10. Intersect(d, a) → D
  11. Segment(A, D) → e
  12. Segment(C, D) → f
  13. Point(xAxis) → F
  14. Point(xAxis) → G
  15. Segment(F, G) → g
  16. Segment(H, I) → h
  17. CircleArc(A, B, C) → k
  18. OrthogonalLine(P, g) → i
  19. Intersect(g, i) → J
  20. Segment(P, J) → j
  21. Segment(F, J) → l
  22. Function(sin(x - 2), 2, 8.3) → f_1
  23. Intersect(f_1, g, (5.14159265360225, -1.2456579871614342E-11)) → K
  24. Intersect(f_1, g, (8.283185307179632, 4.594034846457704E-14)) → L
  25. Segment(C, P) → m
  26. Point(h) → M
  27. Point(h) → N
  28. Point(yAxis) → O
  29. Point(yAxis) → Q
  30. Segment(O, Q) → n
  31. Segment(R, S) → p
  32. OrthogonalLine(T, n) → q
  33. Intersect(q, n) → U
  34. Segment(T, U) → r
  35. Segment(U, O) → s
  36. Segment(D, T) → t
  37. Point(n) → V
  38. Point(n) → W
  39. Point(n) → Y
  40. Point(n) → Z
  41. Point(p) → A_1
  42. Point(p) → B_1
  43. Segment(C_1, D_1) → a_1
  44. Segment(E_1, F_1) → b_1
  45. Point(g) → G_1
  46. Point(g) → H_1
  47. OrthogonalLine(G_1, b_1) → c_1
  48. OrthogonalLine(H_1, b_1) → d_1
  49. Intersect(b_1, c_1) → I_1
  50. Intersect(b_1, d_1) → J_1
  51. Point(c_1) → K_1
  52. Point(d_1) → L_1
  53. Segment(K_1, I_1) → e_1
  54. Segment(J_1, L_1) → g_1
  55. Point(b_1) → M_1
  56. Point(b_1) → N_1
  57. Point(b_1) → O_1
  58. Point(b_1) → P_1
  59. Point(b_1) → Q_1
  60. Point(b_1) → R_1
  61. Point(a_1) → S_1
  62. Point(a_1) → T_1
  63. Segment(I_1, U_1) → h_1
  64. Segment(W_1, J_1) → i_1
  65. OrthogonalLine(V_1, b_1) → j_1
  66. Intersect(j_1, b_1) → Y_1
  67. Segment(E_1, Y_1) → k_1
  68. Segment(A, Z_1) → l_1
  69. OrthogonalLine(Z_1, l_1) → m_1
  70. Line(A, C) → n_1
  71. Intersect(m_1, n_1) → A_2
  72. Segment(Z_1, A_2) → p_1
  73. Segment(Z_1, A_2) → q_1
  74. Segment(A, A_2) → r_1
  75. Segment(A_2, V_1) → s_1
  76. Segment(V_1, Y_1) → t_1
  77. Segment(A, B_2) → a_2
  78. Segment(C, D) → b_2
  79. Polygon(N, C_2, D_2, M) → poly1, n_2, c_2, d_2, m_2
  80. Intersect(g, h) → G_2
  81. Intersect(h, m_2) → H_2
  82. Polygon(B_1, I_2, J_2, A_1) → poly2, b_3, i_2, j_2, a_3
  83. Point(a_1) → L_2
  84. Point(a_1) → M_2
  85. Mirror(I_1, a_1) → N_2
  86. Segment(O_2, P_2) → e_2
  87. Polygon(O_2, K_1, U_1, P_2) → poly3, o_2, k_2, u_1, p_2