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单位圆与六种三角函数

单位圆与六种三角函数
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2016-05-18 08:12
圆函数三角函数几何作图函数图像
①本范例通过动态演示单位圆，展示角度θ与三角函数值（正弦、余弦、正切等）的几何关系；②涉及核心数学概念包括单位圆、三角函数定义、直角三角形边长关系；③作图要点：使用Point, Line, Circle, Tangent, Slider等命令绘制单位圆、坐标轴、三角函数线段，并动态关联θ与函数值；④适合高中数学教学，用于直观理解三角函数定义与性质。

GeoGebra 命令及参数

  1. Point(xAxis) → B
  2. Point(yAxis) → C
  3. Point(yAxis) → D
  4. Line(D, C) → Yaxis
  5. Line(D, B) → Xaxis
  6. OrthogonalLine(A, Xaxis) → XequalsCosine_1
  7. Intersect(Xaxis, XequalsCosine_1) → XequalsCosine
  8. Circle(D, B) → UnitCircle
  9. Tangent(A, UnitCircle) → TangentToA,
  10. Intersect(Yaxis, TangentToA) → YequalsCosecant
  11. Intersect(Xaxis, TangentToA) → XequalsSecant
  12. Segment(D, A) → f
  13. Segment(D, XequalsCosine) → Cosineθ
  14. Segment(XequalsCosine, A) → Sineθ
  15. Segment(A, XequalsSecant) → Tangentθ
  16. Segment(A, YequalsCosecant) → Cotangentθ
  17. Segment(D, YequalsCosecant) → Cosecantθ
  18. Segment(D, XequalsSecant) → Secantθ
  19. OrthogonalLine(A, Sineθ) → YequalsSine
  20. Point(YequalsSine) → H
  21. OrthogonalLine(yequalsx, xAxis) → xequalsθ
  22. Intersect(YequalsSine, xequalsθ) → DerivedSine
  23. Intersect(TangentToA, yAxis) → YequalsCosecant2
  24. OrthogonalLine(YequalsCosecant2, yAxis) → YequalsCosecant_1
  25. Intersect(xequalsθ, YequalsCosecant_1) → DerivedCosecant
  26. OrthogonalLine(yequalsx, xequalsθ) → yequalsθ
  27. Intersect(XequalsCosine_1, yequalsθ) → SidewaysCosine
  28. Intersect(f, Cosineθ) → L
  29. Line(L, yequalsx) → YequalsX
  30. OrthogonalLine(SidewaysCosine, YequalsX) → ReflectsSidewaysCosine
  31. Intersect(xequalsθ, ReflectsSidewaysCosine) → DerivedCosine
  32. OrthogonalLine(XequalsSecant, yequalsθ) → XequalsSecant_1
  33. Intersect(yequalsθ, XequalsSecant_1) → SidewaysSecant
  34. OrthogonalLine(SidewaysSecant, YequalsX) → ReflectsSidewaysSecant
  35. Intersect(xequalsθ, ReflectsSidewaysSecant) → DerivedSecant
  36. OrthogonalLine(B, Secantθ) → Xequals1
  37. Line(D, A) → a
  38. Intersect(Xequals1, a) → YequalsTangent
  39. OrthogonalLine(YequalsTangent, Xequals1) → YequalsTangent_1
  40. Intersect(xequalsθ, YequalsTangent_1) → DerivedTangent
  41. OrthogonalLine(C, Cosecantθ) → Yequals1
  42. Intersect(a, Yequals1) → XequalsCotangent_1
  43. OrthogonalLine(XequalsCotangent_1, Yequals1) → XequalsCotangent
  44. Intersect(yequalsθ, XequalsCotangent) → SidewaysCotangent
  45. OrthogonalLine(SidewaysCotangent, YequalsX) → ReflectsSidewaysCotangent
  46. Intersect(xequalsθ, ReflectsSidewaysCotangent) → DerivedCotangent