MathPlotAI Logo MathPlotAI

Animation 192: Transformation of Tangent Function

Animation 192: Transformation of Tangent Function
Loading the math board and drawing, please wait…
2017-02-13 00:22
FunctionTrigonometryTransformation
This example demonstrates the transformation of the tangent function, including translation, dilation, and mirroring. Key mathematical concepts include trigonometric functions and function transformations. Using GeoGebra commands such as Mirror, Dilate, Translate, etc., the effects of these transformations can be visually demonstrated. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

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

AI Drawing Prompt Reference

Create an animation of the transformation of the tangent function, including translation, dilation, and mirroring. First, mirror the tangent function, then perform translations and dilations around the x-axis. Draw corresponding segments and arcs. Next, apply multiple dilations and translations to generate a series of transformed images. Finally, use rotations and mirroring to create the final shape.
The prompt above was compiled from the original drawing commands and is for reference only.