积极 AI Logo 积极 AI

正弦、余弦、正切在直角三角形中的含义

正弦、余弦、正切在直角三角形中的含义
几何画板及绘图内容加载中，请稍等……
2017-05-24 00:05
测试改名0三角函数几何作图
所属专题 Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster
①本范例演示了正弦、余弦、正切三种三角函数在直角三角形中的几何意义；②涉及的核心数学概念包括三角函数定义、直角三角形边角关系、几何变换；③作图要点提炼自 GeoGebra 命令：点、线段、垂线、旋转、角度、射线、圆、交点、多边形、文本框、中点、文本旋转、条件判断；④适合高中数学学生学习和理解三角函数基础概念，也可用于几何变换教学。

GeoGebra 命令及参数

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Segment(A, B) → f
  3. OrthogonalLine(B, f) → g
  4. Rotate(B, (a * pi / 180), A) → B'
  5. Angle(B, A, B') → α
  6. Ray(A, B') → h
  7. Circle(B, 2) → c
  8. Intersect(c, g, 2) → C
  9. Ray(B, C) → i
  10. Intersect(h, i) → D
  11. Segment(B, D) → j
  12. Segment(A, D) → k
  13. Polygon(A, B, D) → poly1, d, a_1, b
  14. Rotate(B, If[0 < e ≤ 1, (-((e * (pi / 2 - α)))), α - pi / 2], D) → B'_1
  15. Rotate(D, If[0 < e ≤ 1, (-((e * (pi / 2 - α)))), α - pi / 2], D) → D'
  16. Segment(B'_1, D') → j'
  17. Rotate(A, If[0 < l ≤ 1, (α * l), α], A) → A'
  18. Rotate(B, If[0 < l ≤ 1, (α * l), α], A) → B'_2
  19. Segment(A', B'_2) → f'
  20. Rotate(B, If[0 < m ≤ 1, (m * pi / 2), pi / 2], B) → B'_3
  21. Rotate(D, If[0 < m ≤ 1, (m * pi / 2), pi / 2], B) → D'_1
  22. Segment(B'_3, D'_1) → j'_1
  23. Textfield(a) → InputBox1
  24. Angle(D, B, A) → β
  25. Midpoint(A, D) → E
  26. RotateText(text7, α) → text8
  27. Midpoint(A', B'_2) → F
  28. RotateText(text9, α) → text10
  29. Point(Ray[G, G + (1, 0)]) → H
  30. Segment(G, H) → t
  31. Rotate(H, (a * pi / 180), G) → H'
  32. Ray(G, H') → f_1
  33. OrthogonalLine(H, t) → g_1
  34. Intersect(g_1, f_1) → I
  35. Polygon(G, H, I) → t1, i_1, g_2, h_1
  36. Angle(H, G, I) → γ
  37. Segment(H, I) → j_1
  38. Rotate(H, If[0 < e ≤ 1, ((-e) * (pi / 2 - α)), (-(pi / 2 - α))], I) → H'_{1}
  39. Rotate(I, If[0 < e ≤ 1, ((-e) * (pi / 2 - α)), (-(pi / 2 - α))], I) → I'
  40. Segment(H'_{1}, I') → k_1
  41. Rotate(G, If[0 < l ≤ 1, (l * α), α], G) → G'
  42. Rotate(H, If[0 < l ≤ 1, (l * α), α], G) → H'_{2}
  43. Segment(G', H'_{2}) → t'
  44. Angle(I, H, G) → δ
  45. Rotate(H, If[0 < m ≤ 1, (m * pi / 2), pi / 2], H) → H'_{3}
  46. Rotate(I, If[0 < m ≤ 1, (m * pi / 2), pi / 2], H) → I'_{1}
  47. Segment(H'_{3}, I'_{1}) → l_1
  48. RotateText(text2, atand(Slope[Line[D, A]])) → text16
  49. Textfield(a) → InputBox2
  50. If(e ≠ 0 ∧ (α ≟ pi / 6 ∨ α ≟ pi / 2 ∨ α ≟ 0), "=", "≈") → text6
  51. If(l ≠ 0 ∧ (α ≟ pi / 3 ∨ α ≟ pi / 2 ∨ α ≟ 0), "=", "≈") → text19
  52. If(m ≠ 0 ∧ (α ≟ pi / 4 ∨ α ≟ 0), "=", "≈") → text20