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Animation Demonstrating Trigonometry and Cones

Animation Demonstrating Trigonometry and Cones
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2016-12-01 09:30
FunctionTrigonometrySolid GeometryGeometric Construction
This example visually demonstrates the relationship between the sine function and cones through animation. It involves core math concepts like trigonometric functions, right triangles, linear functions, cones, and sine values. GeoGebra commands such as CircleArc, Point, Circle, Intersect, Ray, CircleSector, Mirror, Angle, Dilate, Segment, Rotate, and Polygon are used in its construction. Suitable for high school mathematics education to understand the connection between trigonometry and solid geometry.

GeoGebra Commands & Parameters

  1. CircleArc(B, A, J) → f_1
  2. CircleArc(B, A, I) → p
  3. Point(p) → C
  4. Circle(B, A) → c
  5. Intersect(f, h) → D
  6. Ray(B, C) → i
  7. CircleArc(B, I, A) → q
  8. CircleArc(B, E, G) → e
  9. Intersect(e, i, 1) → H
  10. CircleSector(B, E, H) → k
  11. Mirror(C, j) → C'
  12. Mirror(H, j) → H'
  13. Angle(E, B, H) → α
  14. Dilate(B, If[0 < b ≤ 1, 1 - b, 0], D) → B'
  15. Segment(B, B') → l
  16. Angle(C, D, B) → β
  17. Mirror(D, j) → D'
  18. Mirror(C, j) → C'_1
  19. Angle(B, D, C') → γ
  20. Rotate(E, If[1 < b ≤ 2, ((b - 1) * α), α], B) → E'
  21. Mirror(E', j) → E''
  22. CircleSector(B, E, E') → r
  23. CircleSector(B, E'', E) → s
  24. Circle(B, 1) → d
  25. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C) → B'_1
  26. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C'_1) → B'_2
  27. CircleArc(B, C', C) → c_1
  28. CircleSector(B, C, C') → d_1
  29. Polygon(B, D, C) → poly1, c_2, b_1, d_2
  30. Polygon(B, C', D) → poly2, d_3, b_2, c'
  31. Circle(B, A) → e_1
  32. Dilate(D, If[1 < b ≤ 2, 2 - b, 0], C) → D'_1
  33. Segment(D, D'_1) → m
  34. Mirror(D'_1, y = 0) → K
  35. Point(m) → L
  36. Rotate(D, If[2 < b ≤ 3, ((-(b - 2)) * π), (-π)], D) → D'_2
  37. Rotate(D'_1, If[2 < b ≤ 3, ((-(b - 2)) * π), (-π)], D) → M
  38. Segment(D'_2, M) → m'
  39. Segment(B, C) → n
  40. Point(n) → N
  41. Segment(N, C'_1) → t