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Dynamic Tangent Function Period Illustration

Dynamic Tangent Function Period Illustration
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2017-05-07 07:50
FunctionTrigonometryGeometric ConstructionSlider AnimationGraphing
This example dynamically illustrates the periodic behavior of the tangent function. It involves core math concepts like tangent function period, trigonometric graphs, and geometric transformations. Key GeoGebra commands and objects used include Mirror, Circle, Dilate, Segment, Vector, Translate, Rotate, and CircleArc. Suitable for high school mathematics education to understand function periodicity and geometric transformations.

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