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What 'CO' in COsine Means Interactive Activity

What 'CO' in COsine Means Interactive Activity
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2016-07-11 04:09
AngleFunctionTrigonometryGeometric Construction
In collections Geometry Review Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Trigonometric Identities
This example demonstrates the geometric meaning of sine and cosine in complementary angles. It involves core math concepts: complementary angles, sine function, cosine function, right triangle. Construction highlights include using commands like Segment, Rotate, Ray, OrthogonalLine, Point, Intersect, Angle, Polygon, Circle, CircleSector, Dilate, Vector, Translate in GeoGebra. Suitable for high school mathematics teaching to understand basic properties of trigonometric functions and complementary angle relationships.

GeoGebra Commands & Parameters

  1. Segment(A, C) → adj
  2. Rotate(C, β, A) → B'
  3. Ray(A, B') → d
  4. Ray(A, C) → a_1
  5. OrthogonalLine(C, a_1) → b
  6. Point(b) → C_1
  7. Ray(C, C_1) → c
  8. Intersect(c, d) → D
  9. Segment(C, D) → opp
  10. Min(opp, adj) → o
  11. Angle(C, A, B') → α
  12. Segment(A, D) → hyp
  13. Angle(D, C, A) → γ
  14. Polygon(A, C, D) → poly1, d_1, a, b_1
  15. Rotate(C, If[3 < k ≤ 4, ((-(k - 3)) * (π / 2 - α)), (-(π / 2 - α))], D) → C'
  16. Rotate(D, If[0 < k ≤ 1, ((-k) * (π / 2 - α)), (-(π / 2 - α))], D) → D'
  17. Segment(C', D') → opp'
  18. Ray(A, C) → l
  19. Ray(A, D) → m
  20. Min(opp, hyp) → n
  21. Circle(D, (0.25 * o)) → q
  22. Circle(A, (0.25 * o)) → p
  23. Intersect(p, m) → B,
  24. Intersect(p, l) → E,
  25. Intersect(q, m) → F, G
  26. Intersect(q, opp) → H,
  27. CircleSector(A, E, B) → r
  28. CircleSector(D, F, H) → s
  29. Dilate(D, If[0 < k ≤ 1, 1 - k, 0], C) → D'_1
  30. Vector(D, D'_1) → u
  31. Translate(s, u) → s'
  32. Rotate(s', If[1 < k ≤ 2, ((k - 1) * π), π], C) → s''
  33. Dilate(A, If[2 < k ≤ 3, 3 - k, 0], C) → A'
  34. Vector(A, A') → v
  35. Translate(r, v) → r'
  36. Point(l) → I
  37. Ray(C, I) → t