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单位圆中的三角函数比值

单位圆中的三角函数比值
几何画板及绘图内容加载中，请稍等……
2015-11-30 17:10
圆函数三角函数
该范例展示了六个三角函数的图形及其相关函数图像。通过单位圆，直观地理解正弦、余弦、正切、余切、正割和余割等概念。使用了Circle、Segment、Tangent、Angle、Function等GeoGebra命令进行构造。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Intersect(c, xAxis, 2) → C
  5. Segment(A, C) → d
  6. Point(c) → D
  7. OrthogonalLine(D, d) → f
  8. Tangent(D, c) → e,
  9. Intersect(xAxis, e) → E
  10. Segment(E, A) → m
  11. Angle(C, A, D) → θ
  12. Segment(A, D) → b
  13. Intersect(e, yAxis) → F
  14. Segment(F, D) → cotα
  15. Segment(D, E) → tanα
  16. Segment(A, F) → cscα
  17. Intersect(f, m) → H
  18. Segment(D, H) → sinα
  19. Segment(A, E) → secα
  20. Segment(A, H) → cosα
  21. OrthogonalLine(D, sinα) → i
  22. Function(1 / sin((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → cosecantα
  23. Intersect(cosecantα, h, (2.495559497562619, 1.3880195691190431)) → G
  24. Function(sin((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → sineα
  25. Intersect(sineα, h, (2.495559497562619, 0.7204509376151564)) → I
  26. Function(tan((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → tangentα
  27. Intersect(tangentα, h, (2.495559497562619, 1.0388533504365465)) → J
  28. Function(cos((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → cosineα
  29. Intersect(cosineα, h, (2.495559497562619, 0.6935059094841528)) → K
  30. Function(1 / cos((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → secantα
  31. Intersect(secantα, h, (2.495559497562619, 1.4419487798508095)) → L
  32. Function(1 / tan((2 * (x - (2 * 3.14 / 3)))), 2.09, 5.24) → cotangentα
  33. Intersect(cotangentα, h, (2.495559497562619, 0.9625997736637038)) → M
  34. Function(0, 1.9, 5.5) → g
  35. Segment(A, C) → a
  36. Segment(H, D) → j
  37. Segment(A, F) → k
  38. Segment(F, E) → l
  39. Intersect(j, m) → N
  40. Intersect(m, l) → O
  41. Intersect(k, l) → P
  42. Function(1, 1.9, 5.5) → p
  43. Function(-1, 1.9, 5.5) → q
  44. CircleArc(A, C, D) → f_1
  45. Intersect(sineα, tangentα, (2.0933273569696556, -1.195272735515079E-5)) → Q
  46. Intersect(g, h, 1) → R
  47. Segment(Q, R) → g_1