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三角函数加法公式演示

三角函数加法公式演示
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2015-12-08 17:25
角三角函数几何作图
①本范例通过动态图形演示三角函数加法公式；②涉及核心概念包括三角函数、角度、几何作图；③构造要点：使用 Circle, Point, Polygon, Line, OrthogonalLine, Intersect, Segment, CircleSector, Angle, If 等命令绘制图形并计算；④适合高中数学教学和几何作图学习。

GeoGebra 命令及参数

  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