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Wave Transformation Demo

Wave Transformation Demo
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2013-10-18 04:15
VectorFunctionTrigonometryCoordinate Geometry
This example demonstrates the transformation of a sine function graph through translation and rotation in a plane. It involves core mathematical concepts such as trigonometry, translation, rotation, line segments, and equilateral triangles. Key GeoGebra commands/objects used include CurveCartesian, Vector, Sequence, Element, Circle, Intersect, and Segment. Suitable for high school students studying analytical geometry and trigonometric transformations.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, f(t), t, If[bm, ((-π) * m), 0], (π * m)) → g
  2. Vector(A, C) → u
  3. Sequence(Translate[Rotate[g, ((((kpu + kpd) * i) * 2) * π) + kr], Vector[(i * u)]], i, 1 / n, 1, 1 / n) → liste2
  4. Element(liste2, 1) → c1
  5. Element(liste2, 2) → c2
  6. Element(liste2, 3) → c3
  7. Element(liste2, 4) → c4
  8. Element(liste2, 5) → c5
  9. Element(liste2, 6) → c6
  10. Element(liste2, 7) → c7
  11. Element(liste2, 8) → c8
  12. Element(liste2, 9) → c9
  13. Element(liste2, 10) → c10
  14. Element(liste2, 11) → c11
  15. Element(liste2, 12) → c12
  16. Element(liste2, 13) → c13
  17. Element(liste2, 14) → c14
  18. Element(liste2, 15) → c15
  19. Element(liste2, 16) → c16
  20. Element(liste2, 17) → c17
  21. Element(liste2, 18) → c18
  22. Element(liste2, 19) → c19
  23. Element(liste2, 20) → c20
  24. Element(liste2, 21) → c21
  25. Element(liste2, 22) → c22
  26. Element(liste2, 23) → c23
  27. Element(liste2, 24) → c24
  28. Element(liste2, 25) → c25
  29. Element(liste2, 26) → c26
  30. Element(liste2, 27) → c27
  31. Element(liste2, 28) → c28
  32. Element(liste2, 29) → c29
  33. Element(liste2, 30) → c30
  34. Element(liste2, 31) → c31
  35. Element(liste2, 32) → c32
  36. Element(liste2, 33) → c33
  37. Element(liste2, 34) → c34
  38. Element(liste2, 35) → c35
  39. Element(liste2, 36) → c36
  40. Element(liste2, 37) → c37
  41. Element(liste2, 38) → c38
  42. Element(liste2, 39) → c39
  43. Element(liste2, 40) → c40
  44. Element(liste2, 41) → c41
  45. Element(liste2, 42) → c42
  46. Element(liste2, 43) → c43
  47. Element(liste2, 44) → c44
  48. Element(liste2, 45) → c45
  49. Element(liste2, 46) → c46
  50. Element(liste2, 47) → c47
  51. Element(liste2, 48) → c48
  52. Circle(R, V) → e
  53. Circle(V, R) → h
  54. Intersect(e, h) → B, B_1, ,
  55. Circle(B, R) → k
  56. Segment(D, R) → dr
  57. Segment(D, V) → dv
  58. Segment(D, B) → db
  59. Segment(R, V) → rv
  60. Segment(E, R) → er
  61. Segment(E, V) → ev
  62. Segment(E, B) → eb
  63. Vector(Pt, C) → w
  64. Vector(Pt, A) → z
  65. Vector(Pc, E) → i
  66. Vector(Pc, D) → j

AI Drawing Prompt Reference

Draw a sine function graph and then translate and rotate it using vectors to demonstrate the transformation process, including multiple translated and rotated images of the function graph, along with the vectors and parallelograms used for the transformations, finally connecting these images with line segments to form a complete transformation demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.