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Visual Proof of Sine and Cosine Addition Formulae

Visual Proof of Sine and Cosine Addition Formulae
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2015-08-07 06:55
VectorFunctionTrigonometryCoordinate GeometryGeometric Construction
This example visually demonstrates the geometric proof of sine and cosine addition formulae through dynamic illustrations. It involves core math concepts like trigonometric functions, vectors, geometric transformations, and coordinate geometry. The construction utilizes GeoGebra commands such as Intersect, Rotate, Angle, Line, Segment, OrthogonalLine, and RotateText. Suitable for high school and above students to intuitively understand trigonometric identities.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Rotate(A, -90*°, B) → A'
  3. Angle(A', B, A) → α
  4. Line(A', B) → a
  5. Intersect(c, a, 1) → C
  6. Segment(C, A) → b
  7. Segment(C, B) → d
  8. Segment(C, E) → e
  9. Segment(B, D) → f
  10. Segment(B, A) → g
  11. Segment(B, F) → h
  12. Segment(A, D) → i
  13. Angle(E, A, B) → β
  14. Angle(B, A, C) → γ
  15. Angle(F, C, B) → δ
  16. Angle(F, B, A) → ε
  17. OrthogonalLine(C, e) → j
  18. OrthogonalLine(A, i) → k
  19. Intersect(j, k) → G
  20. Segment(G, A) → l
  21. Segment(G, C) → m
  22. Angle(B, D, A) → ζ
  23. Angle(B, F, C) → η
  24. Angle(A, G, C) → θ
  25. Angle(C, E, A) → ι
  26. RotateText(text11, 270*°) → text12
  27. RotateText(text6, 270*°) → text13
  28. RotateText(text15, 90*°) → text16