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单位圆操作演示

单位圆操作演示
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2016-07-04 05:40
圆三角函数矩阵变换几何作图
①本范例通过交互式演示单位圆上的点、角度与三角函数值的关系；②涉及核心数学概念包括三角函数、单位圆、几何变换、矩阵运算；③作图要点提炼自构造摘要，使用了Intersect, Circle, Point, Segment, Angle, Slope, Rotate等GeoGebra命令及对象；④适合高中数学教学，用于理解三角函数与几何图形的关联，提升可视化学习效果。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → UnitCircle
  3. Point(UnitCircle) → C
  4. Segment(A, C) → f
  5. Segment(A, CosAlphaAndSinAlpha) → AlphaSegment
  6. Angle(C, A, CosAlphaAndSinAlpha) → AngleAlpha
  7. Segment(A, CosBetaAndSinBeta) → BetaSegment
  8. Angle(C, A, CosBetaAndSinBeta) → AngleBeta
  9. Slope(AlphaSegment) → TanAlpha
  10. Slope(BetaSegment) → TanBeta
  11. Intersect(UnitCircle, i, 2) → CosGammaAndSinGamma
  12. Intersect(UnitCircle, i, 1) → CosGammaPlus180AndSinGammaPlus180
  13. Segment(CosGammaAndSinGamma, CosGammaPlus180AndSinGammaPlus180) → j
  14. Angle(C, A, CosGammaAndSinGamma) → AngleGamma
  15. Slope(i) → TanGamma
  16. Segment(A, CosGammaAndSinGamma) → GammaSegment
  17. Segment(A, CosGammaPlus180AndSinGammaPlus180) → GammaSegmentTwo
  18. Rotate(C, Theta, A) → CosThetaAndSinTheta
  19. Angle(C, A, CosThetaAndSinTheta) → AngleTheta
  20. Segment(A, CosThetaAndSinTheta) → ThetaSegment
  21. Slope(ThetaSegment) → TanTheta