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Sine and Cosecant Functions Special Property

Sine and Cosecant Functions Special Property
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2016-11-30 17:58
AngleFunctionTrigonometryGeometric ConstructionGraphing
In collections Trigonometric Identities
This example dynamically demonstrates the relationship between sine and cosecant functions, visually showcasing trigonometric function graphs and properties. Core math concepts include sine function, cosecant function, trigonometric identities, and geometric proofs. Construction highlights the use of GeoGebra commands/objects like Circle, CircleArc, Point, Intersect, Ray, CircleSector, Mirror, Angle, Dilate, Segment, Rotate, Polygon. Suitable for high school mathematics teaching to understand trigonometric function transformations and identity proofs.

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. Segment(B, B'_1) → n
  28. Segment(B, B'_2) → t
  29. CircleArc(B, C', C) → c_1
  30. CircleSector(B, C, C') → d_1
  31. Polygon(B, D, C) → poly1, c_2, b_1, d_2
  32. Polygon(B, C', D) → poly2, d_3, b_2, c'
  33. Circle(B, A) → e_1
  34. Dilate(D, If[1 < b ≤ 2, 2 - b, 0], C) → D'_1
  35. Segment(D, D'_1) → m
  36. Mirror(D'_1, y = 0) → K
  37. Point(m) → L
  38. Segment(L, K) → g_1

AI Drawing Prompt Reference

Draw a dynamic graph demonstrating the relationship between sine and cosecant functions, featuring a circle and arcs, defining angles with points and rays, using reflections and rotations to construct symmetric shapes, and showcasing the graphs and properties of sine and cosecant functions for high school trigonometric transformations and identity proofs.
The prompt above was compiled from the original drawing commands and is for reference only.