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单位圆 by Hans Lehman

单位圆 by Hans Lehman
几何画板及绘图内容加载中，请稍等……
2018-05-29 21:33
圆三角函数几何作图
该范例展示了单位圆的构造。涉及的核心数学概念包括圆的性质和三角函数。通过使用GeoGebra命令如Sequence、Intersect、Circle等，可以动态地展示单位圆上的点和角度关系。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Sequence(FractionText[k / fractionsofpie], k, 1, advancedpointoncircle) → list5
  2. Sequence(FractionText[(k * 180 / fractionsofpie)], k, 1, advancedpointoncircle) → list7
  3. Sequence(((r * cos((k * π / fractionsofpie))), (r * sin((k * π / fractionsofpie)))), k, 1, advancedpointoncircle) → list3
  4. Sequence(Text[(((Element[list5, t] * "π=") * Element[list7, t]))°, (x(Element[list3, t]) + movlabelshorizontally, y(Element[list3, t]) + movelabelsvertically), false, true], t, 1, (2 * fractionsofpie)) → list6
  5. Sequence(Text[(("cos(" * FractionText[k / fractionsofpie]) * " π )="), (0, 0), false, true], k, 1, advancedpointoncircle) → list8
  6. Intersect(xAxis, yAxis) → A
  7. Circle(A, 1) → c
  8. Textfield(fractionsofpie) → inputBox1
  9. Circle((0, 0), r) → d
  10. Sequence(Text[((((("$\frac{" * 2) * π) * "}{") * fractionsofpie) * "}$"), Element[list3, t], false, true], t, 1, Length[list3]) → list4
  11. FractionText((2 / fractionsofpie * π)) → text2
  12. Textfield(r) → inputBox2
  13. Textfield(advancetriangletonextangle) → inputBox3
  14. Segment((0, 0), C) → e
  15. Segment(C, B) → f
  16. Segment(A, B) → g
  17. Simplify(newforcosine) → h
  18. Segment(A, B) → i
  19. Angle(C, A, B) → α
  20. FractionText(2 / fractionsofpie) → text4
  21. Angle(E, A, B) → β
  22. TrigExpand(sin((2 * x))) → p
  23. Angle(C, A, B) → γ
  24. Mod(375, 360) → l
  25. Sequence((cos((k * π / fractionsofpie)), sin((k * π / fractionsofpie))), k, 0, (2 * fractionsofpie)) → list1
  26. Sequence(Segment[(0, 0), (cos((k * π / fractionsofpie)), sin((k * π / fractionsofpie)))], k, 1, (2 * fractionsofpie)) → list2
  27. Dimension(list6) → m
  28. Dimension(list6) → n
  29. Point(i) → F
  30. Sequence(Text["\frac{\sqrt{2}}{2}", (k, 0), false, true], k, 1, 4) → list9
  31. Sequence(Text[(((Element[list5, t] * "π=") * Element[list7, t]))°, (x(Element[list3, t]) + movlabelshorizontally, y(Element[list3, t]) + movelabelsvertically), false, true], t, 1, advancedpointoncircle) → list12
  32. Sequence(cos((k * π / fractionsofpie)), k, 1, advancedpointoncircle) → list13
  33. CurveCartesian(((1 / 10 + t / 100) * cos((t * π / fractionsofpie))), ((1 / 10 + t / 100) * sin((t * π / fractionsofpie))), t, 0, advancedpointoncircle) → q
  34. Sequence(Text[(("sin(" * FractionText[k / fractionsofpie]) * " π )="), (0, 0), false, true], k, 1, advancedpointoncircle) → list14
  35. Sequence(sin((k * π / fractionsofpie)), k, 1, advancedpointoncircle) → list15
  36. Sequence(Angle[Element[list1, t], (0, 0), Element[list1, t + 1]], t, 1, Length[list1]) → list17
  37. Sequence(Text[(("tan(" * FractionText[k / fractionsofpie]) * " π )="), (0, 0), false, true], k, 1, advancedpointoncircle) → list18
  38. Sequence(tan((k * π / fractionsofpie)), k, 1, advancedpointoncircle) → list19
  39. TableText({list12, list8, list13, list14, list15, list18, list19}, "v") → text5
  40. Sequence(((r / 3 * cos((π / fractionsofpie * k))), (r / 3 * sin((π / fractionsofpie * k)))), k, 0, (2 * fractionsofpie), 0.5) → list20
  41. Sequence(Element[list20, t], t, 0, Length[list20], 2) → list22
  42. Sequence(Text[(("\frac{π}{" * fractionsofpie) * "}"), (x(Element[list22, k]) + movlabelshorizontally, y(Element[list22, k]) + movelabelsvertically), false, true], k, 1, Length[list22], 1) → list21
  43. Sequence(Text[(((Element[list5, t] * "π=") * Element[list7, t]))°, (x(Element[list3, t]) + movlabelshorizontally, y(Element[list3, t]) + movelabelsvertically), false, true], t, Length[list6] + 1, advancedpointoncircle) → secondsetpiover4
  44. Segment((-999.9714194038698, 0), (1000.0285805961302, 0)) → a_1
  45. Segment((0, -100), (0, 100)) → b_1
  46. Sequence(((k * π / fractionsofpie), 0), k, -100, 100) → list23
  47. Sequence(Text[(((("\frac{" * k) * "π}{") * fractionsofpie) * "}"), ((k * π / fractionsofpie), 0), false, true], k, -100, 100) → list24
  48. Sequence(Line[((k * π / 2), 0), ((k * π / 2), 1)], k, -100, 100) → list25