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Sine & Cosine Period Dynamic Demo

Sine & Cosine Period Dynamic Demo
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2017-05-05 04:30
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the periodicity of sine and cosine functions. It involves core math concepts: trigonometric period, unit circle, isosceles triangles, coordinate geometry. Construction highlights include commands like Mirror, Circle, Dilate, Segment, Vector, Translate, Rotate, CircleArc, and objects like b, g, h, A, etc. Suitable for high school mathematics teaching to understand trigonometric graphs and properties.

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[3.5 < a ≤ 4.5, 4.5 - a, 0], H) → D'_1
  17. Vector(D, D'_1) → v
  18. Translate(D, v) → D'_2
  19. Translate(D', v) → D''_1
  20. Segment(D'_2, D''_1) → k'
  21. Translate(E, v) → E'
  22. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], E) → D'_3
  23. Vector(D, D'_3) → w
  24. Translate(D'_2, w) → I
  25. Translate(D''_1, w) → J
  26. Segment(I, J) → k''
  27. Translate(p, w) → p_1
  28. Translate(E', w) → E''
  29. Dilate(D, If[3.5 < a ≤ 4.5, 4.5 - a, 0], K) → D'_4
  30. Vector(D, D'_4) → m
  31. Translate(D, m) → D'_5
  32. Translate(D', m) → D''_2
  33. Segment(D'_5, D''_2) → k'_1
  34. Translate(E, m) → E'_1
  35. Translate(D'_5, w) → L
  36. Translate(D''_2, w) → M
  37. Segment(L, M) → n
  38. Translate(f_1, w) → q_1

AI Drawing Prompt Reference

Create a dynamic illustration showing the periodicity of sine and cosine functions, incorporating the unit circle, isosceles triangles, and coordinate geometry elements. Begin by drawing a unit circle, then use operations like mirroring, dilation, translation, and rotation to create multiple auxiliary lines and arcs, demonstrating the periodic relationship between the sine and cosine functions. The graphic should clearly display the geometric connections between the function graphs, the unit circle, and isosceles triangles, suitable for high school mathematics teaching to understand trigonometric properties and graphs.
The prompt above was compiled from the original drawing commands and is for reference only.