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Demonstration of Trigonometric Addition Formulas

Demonstration of Trigonometric Addition Formulas
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2015-12-08 17:25
AngleTrigonometryGeometric Construction
This example dynamically demonstrates trigonometric addition formulas through geometric constructions. It involves core concepts like trigonometric functions, angles, and geometric constructions using commands such as Circle, Point, Polygon, Line, OrthogonalLine, Intersect, Segment, CircleSector, Angle, If. Suitable for high school mathematics education and geometric construction learning.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → circle
  2. Point(circle) → B
  3. Point(circle) → DD
  4. Point(circle) → D
  5. Polygon(A, B, C, D) → sinApB, a, b_2, c, d
  6. Line(A, DD) → redLot
  7. OrthogonalLine(D, redLot) → m
  8. OrthogonalLine(B, redLot) → n
  9. Intersect(m, redLot) → M
  10. Intersect(n, redLot) → N
  11. Line(A, B) → greenLot
  12. Line(M, greenLot) → parallel
  13. Segment(B, N) → redHoehe
  14. Intersect(Line[C, Vector[D, M]], parallel) → E
  15. Polygon(M, E, C, D) → sinAcosB, e, f, g, h
  16. Polygon(M, A, B, E) → cosAsinB, m_1, a_1, b_1, e_1
  17. Segment(D, Intersect[OrthogonalLine[D, greenLot], greenLot]) → greenHoehe
  18. Intersect(redLot, Line[C, E]) → CE
  19. Segment(M, CE) → blueHoehe
  20. Line(C, E) → blueLot
  21. Segment(B, E) → redGrund_1
  22. Segment(C, E) → blueGrund_1
  23. Segment(A, M) → redGrund_2
  24. Segment(D, M) → blueGrund_2
  25. Segment(A, B) → greenGrund_1
  26. Segment(C, D) → greenGrund_2
  27. Intersect(circle, Ray[A, Midpoint[Segment[B, DD]]]) → mBDD,
  28. Intersect(circle, Ray[A, Midpoint[Segment[D, DD]]]) → mBD,
  29. CircleSector(A, DD / 5, D / 5) → angA
  30. CircleSector(A, B / 5, DD / 5) → angB
  31. Angle(D, A, DD) → al
  32. If(al > 180°, (0.1 * mBD), ((-0.1) * mBD)) → Palpha
  33. Angle(DD, A, B) → bl
  34. If(bl > 180°, (0.1 * mBDD), ((-0.1) * mBDD)) → Pbeta