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Dynamic Sine & Cosine Period Demo

Dynamic Sine & Cosine Period Demo
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2017-02-12 12:04
FunctionTrigonometryGraphing
This example dynamically illustrates the periodicity of sine and cosine functions, allowing parameter adjustments to observe periodic changes in function graphs. Key math concepts include trigonometric functions, periodicity, and graphical transformations. Construction involves commands like Mirror, Circle, Dilate, Segment, Vector, Translate, Rotate, CircleArc, and objects such as b, g, h, A, etc. Suitable for high school mathematics teaching to enhance understanding of trigonometric graphs and properties through visualization.

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

Draw a dynamic illustration showing the periodicity of sine and cosine functions, allowing parameter adjustments to observe periodic changes in function graphs. The graph includes a circle and a vector, with the circle being translated and rotated by the vector to generate multiple arcs, and the vector connecting and transforming graph elements to demonstrate symmetry and periodicity.
The prompt above was compiled from the original drawing commands and is for reference only.