MathPlotAI Logo MathPlotAI

Dynamic Demonstration of Tangent Function Periodicity

Dynamic Demonstration of Tangent Function Periodicity
Loading the math board and drawing, please wait…
2017-02-13 00:14
CircleFunctionTrigonometryTransformationGeometric Construction
This example dynamically demonstrates the periodicity of the tangent function and its geometric interpretation. Core concepts include trigonometric functions, unit circle symmetry, and numerical relationships. Construction utilizes GeoGebra commands such as Mirror, Circle, Dilate, Segment, Vector, Translate, Rotate, CircleArc, and Midpoint to create interactive elements. Suitable for high school mathematics instruction or student self-exploration of trigonometric graph characteristics, aiding in understanding periodicity and symmetry.

GeoGebra Commands & Parameters

  1. Mirror(C, x = 0) → C'_1
  2. Circle(B, 1 / b) → d
  3. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], F) → B'
  4. Segment(B, B') → j
  5. Dilate(D, If[1 < a ≤ 2, 2 - a, 0], E) → D'
  6. Segment(D, D') → k
  7. Vector(D, D') → u
  8. Translate(d, u) → d'
  9. Translate(B, u) → B'_1
  10. Translate(G, u) → G'
  11. Rotate(D', If[1 < a ≤ 2, (((-(a - 1)) * 2) * π), (-2 * π)], B'_1) → D''
  12. CircleArc(B'_1, D', D'') → c
  13. Translate(B, u) → B'_2
  14. Translate(B', u) → B''
  15. Segment(B'_2, B'') → j'
  16. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], E) → D'_3
  17. Vector(D, D'_3) → w
  18. Translate(p, w) → p_1
  19. Dilate(D, If[3.5 < a ≤ 4.5, 4.5 - a, 0], K) → D'_4
  20. Vector(D, D'_4) → m
  21. Translate(D, m) → D'_5
  22. Translate(D', m) → D''_2
  23. Segment(D'_5, D''_2) → k'_1
  24. Translate(E, m) → E'_1
  25. Translate(D'_5, w) → L
  26. Translate(D''_2, w) → M
  27. Segment(L, M) → n
  28. Translate(f_1, w) → q_1
  29. Midpoint(k) → N
  30. Dilate(D, If[3.5 < a ≤ 4.5, 4.5 - a, 0], N) → D'_1
  31. Segment(D, D'_1) → i_1
  32. Dilate(N, If[4.5 < a ≤ 5.5, 5.5 - a, 0], E) → N'
  33. Segment(N, N') → j_1
  34. Rotate(D, If[5.5 < a ≤ 6.5, ((a - 5.5) * π), π], N) → D'_2
  35. Rotate(D'_1, If[5.5 < a ≤ 6.5, ((a - 5.5) * π), π], N) → I
  36. Segment(D'_2, I) → k_1
  37. Dilate(D, If[8 < a ≤ 9, 9 - a, 0], J) → D'_6
  38. Vector(D, D'_6) → v
  39. Translate(D, v) → D'_7
  40. Translate(D'_1, v) → P
  41. Segment(D'_7, P) → l_1
  42. Dilate(D, If[9.5 < a ≤ 10.5, 10.5 - a, 0], N) → D'_8
  43. Vector(D, D'_8) → u_1
  44. Translate(s_1s, u_1) → h_2
  45. Translate(D'_7, u_1) → Q
  46. Translate(P, u_1) → P'
  47. Segment(Q, P') → m_1
  48. Translate(D'_6, u_1) → R