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Sine Identity Dynamic Illustration

Sine Identity Dynamic Illustration
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2016-11-30 03:55
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically illustrates the special property of the sine function and trigonometric identities. It involves core math concepts like the sine function, trigonometric identities, linear functions, and rational numbers. Construction highlights include using GeoGebra commands such as Mirror, Point, Intersect, Dilate, Segment, Rotate, Vector, and Translate. Suitable for high school mathematics teaching to understand trigonometric function graphs and properties.

GeoGebra Commands & Parameters

  1. Mirror(g, x = 0) → g_1
  2. Point(g) → F
  3. Intersect(h, y = 0) → G
  4. Mirror(G, x = 0) → G'
  5. Mirror(F, A) → F'
  6. Dilate(H, If[0 < e ≤ 1, 1 - e, 0], G) → H'
  7. Segment(H, H') → i
  8. Dilate(G, If[1 < e ≤ 2, 2 - e, 0], F) → G'_1
  9. Segment(G, G'_1) → j
  10. Rotate(H, If[2 < e ≤ 3, ((-(e - 2)) * π), (-π)], H) → H'_1
  11. Rotate(H', If[2 < e ≤ 3, ((-(e - 2)) * π), (-π)], H) → H''
  12. Segment(H'_1, H'') → i'
  13. Dilate(G', If[3 < e ≤ 4, 4 - e, 0], F') → G''
  14. Segment(G', G'') → k
  15. Dilate(F, If[4 < e ≤ 5, 5 - e, 0], F') → F'_1
  16. Vector(F, F'_1) → u
  17. Translate(G, u) → G'_2
  18. Translate(G'_1, u) → I
  19. Mirror(g, A) → g_2
  20. Rotate(G, If[4 < e ≤ 5, ((-(e - 4)) * π), (-π)], G) → G'_3
  21. Rotate(G'_1, If[4 < e ≤ 5, ((-(e - 4)) * π), (-π)], G) → J
  22. Segment(G'_3, J) → j'
  23. Dilate(G, If[5 < e ≤ 6, 6 - e, 0], G') → G'_4
  24. Vector(G, G'_4) → v
  25. Translate(G'_3, v) → K
  26. Translate(J, v) → J'
  27. Segment(K, J') → j''