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Sine Function Graph and Limits

Sine Function Graph and Limits
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2018-07-22 06:32
FunctionTrigonometryLimit
In collections Homothety, Rotation Symmetry -RO
This example demonstrates the graph of the sine function and the concept of limits. By constructing the sine function graph, it helps understand the periodicity and amplitude characteristics of the function. Using GeoGebra commands such as Segment, OrthogonalLine, Point, etc., it illustrates the process of drawing function graphs. Suitable for high school mathematics education, aiding students in understanding basic concepts of function graphs and limits.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → C
  5. OrthogonalLine(C, g) → i
  6. Intersect(h, i) → D
  7. Polygon(C, D, B, A) → q1, c, d, b, a
  8. Polygon(C, B, D) → t1, d_1, c_1, b_1
  9. AngularBisector(D, C, B) → j
  10. Segment(D, A) → k
  11. Intersect(k, d_1) → E
  12. Point(k) → F
  13. Dilate(C, 9 / 10, F) → C'
  14. Dilate(B, 9 / 10, F) → B'
  15. Dilate(D, 9 / 10, F) → D'
  16. Polygon(C', B', D') → t1', d', c', b'
  17. Dilate(C, 8 / 10, F) → C'_1
  18. Dilate(B, 8 / 10, F) → B'_1
  19. Dilate(D, 8 / 10, F) → D'_1
  20. Polygon(C'_1, B'_1, D'_1) → t1'_1, d'_1, c'_1, b'_1
  21. Dilate(C, 7 / 10, F) → C'_2
  22. Dilate(B, 7 / 10, F) → B'_2
  23. Dilate(D, 7 / 10, F) → D'_2
  24. Polygon(C'_2, B'_2, D'_2) → t1'_2, d'_2, c'_2, b'_2
  25. Dilate(C, 6 / 10, F) → C'_3
  26. Dilate(B, 6 / 10, F) → B'_3
  27. Dilate(D, 6 / 10, F) → D'_3
  28. Polygon(C'_3, B'_3, D'_3) → t1'_3, d'_3, c'_3, b'_3
  29. Dilate(C, 5 / 10, F) → C'_4
  30. Dilate(B, 5 / 10, F) → B'_4
  31. Dilate(D, 5 / 10, F) → D'_4
  32. Polygon(C'_4, B'_4, D'_4) → t1'_4, d'_4, c'_4, b'_4
  33. Dilate(C, 4 / 10, F) → C'_5
  34. Dilate(B, 4 / 10, F) → B'_5
  35. Dilate(D, 4 / 10, F) → D'_5
  36. Polygon(C'_5, B'_5, D'_5) → t1'_5, d'_5, c'_5, b'_5
  37. Dilate(C, 3 / 10, F) → C'_6
  38. Dilate(B, 3 / 10, F) → B'_6
  39. Dilate(D, 3 / 10, F) → D'_6
  40. Polygon(C'_6, B'_6, D'_6) → t1'_6, d'_6, c'_6, b'_6
  41. Dilate(C, 2 / 10, F) → C'_7
  42. Dilate(B, 2 / 10, F) → B'_7
  43. Dilate(D, 2 / 10, F) → D'_7
  44. Polygon(C'_7, B'_7, D'_7) → t1'_7, d'_7, c'_7, b'_7
  45. Mirror(C', E) → C''
  46. Mirror(B', E) → B''
  47. Mirror(D', E) → D''
  48. Polygon(C'', B'', D'') → t1'', d'', c'', b''
  49. Mirror(C', E) → C''_1
  50. Mirror(B', E) → B''_1
  51. Mirror(D', E) → D''_1
  52. Mirror(C'_1, E) → G
  53. Mirror(B'_1, E) → H
  54. Mirror(D'_1, E) → I
  55. Polygon(G, H, I) → t2, i_1, g_1, h_1
  56. Mirror(C'_2, E) → J
  57. Mirror(B'_2, E) → K
  58. Mirror(D'_2, E) → L
  59. Polygon(J, K, L) → t3, l, j_1, k_1
  60. Mirror(C'_3, E) → M
  61. Mirror(B'_3, E) → N
  62. Mirror(D'_3, E) → O
  63. Polygon(M, N, O) → t4, o, m, n
  64. Mirror(C'_4, E) → P
  65. Mirror(B'_4, E) → Q
  66. Mirror(D'_4, E) → R
  67. Polygon(P, Q, R) → t5, r, p, q
  68. Mirror(C'_5, E) → S
  69. Mirror(B'_5, E) → T
  70. Mirror(D'_5, E) → U
  71. Polygon(S, T, U) → t6, u, s, t
  72. Mirror(C'_6, E) → V
  73. Mirror(B'_6, E) → W
  74. Mirror(D'_6, E) → Z
  75. Polygon(V, W, Z) → t7, z_1, v, w
  76. Mirror(C'_7, E) → A_1
  77. Mirror(B'_7, E) → B_1
  78. Mirror(D'_7, E) → C_1
  79. Polygon(A_1, B_1, C_1) → t8, c_2, a_1, b_2