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单位圆演示 by Tom Owsiak

单位圆演示 by Tom Owsiak
几何画板及绘图内容加载中，请稍等……
2013-04-21 11:03
圆函数三角函数解析几何参数方程
①本范例演示单位圆的构造及其与三角函数的关系；②涉及核心数学概念包括圆、三角函数（正弦、余弦）、参数方程、解析几何；③构造要点运用了GeoGebra命令如Sequence（数列）、Intersect（交点）、Circle（圆）、Textfield（文本框）、Segment（线段）、Simplify（化简）、Angle（角度）、TrigExpand（三角展开）、Mod（模运算）、Point（点）、CurveCartesian（笛卡尔曲线）、TableText（表格文本）、Text（文本）等；④适合高中及以上学生学习和理解三角函数、解析几何及参数方程。

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[(π / 2 + k * π, 0), (π / 2 + k * π, 1)], k, -100, 100) → list25
  49. Text("\frac{\sqrt{2}}{2}", (0, 0), false, true) → text3
  50. Segment(G, H) → i_1
  51. Segment(G, J) → j_1
  52. Sequence(Line[(k * π, 0), (k * π, 1)], k, -100, 100) → list31

AI 绘图提示语参考

绘制单位圆，包括圆心在原点的圆、正弦和余弦函数的图像以及角度标记。首先画一个半径为1的单位圆，然后绘制从圆心到圆周上点的线段，标注角度和对应的正弦、余弦值。接着画x轴和y轴，以及圆周上等分点的度数标记。
以上提示语为根据原始绘图命令整理而来，仅供参考。