积极 AI Logo 积极 AI

一般角的三角比自我评估

一般角的三角比自我评估
几何画板及绘图内容加载中，请稍等……
2017-02-10 18:17
角函数三角函数
①本范例演示了如何绘制和计算任意角度的三角比；②涉及的核心数学概念包括三角函数、参考角、一般角等；③作图要点使用了GeoGebra命令如Intersect, Angle, Segment, Polygon等；④适合高中数学教学和自学，用于理解和应用三角函数知识。

GeoGebra 命令及参数

  1. Intersect(c, xAxis, 1) → C
  2. Intersect(c, xAxis, 2) → A
  3. Intersect(xAxis, yAxis) → O
  4. If(m, θ_{debug}, If[counter < 11, (15 * Random[25, 48]), If[counter < 21, (5 * Random[73, 288]), (15 * Random[-48, -25])]]) → θ_{random}
  5. Angle(A, O, P) → ReferenceAngle1
  6. Angle(C, O, P) → ReferenceAngle2
  7. If(ReferenceAngle1 < 90.01°, ReferenceAngle1, ReferenceAngle2) → E3
  8. Angle(A, O, P) → α_+
  9. Segment(O, A) → a
  10. Segment(O, P) → b
  11. Angle(A, O, P_o) → θ_c
  12. Angle(P, O, A) → α_-
  13. Segment(O, C) → d
  14. If(ReferenceAngle1 ≟ 0°, 1, floor((θ_o - 0.01) / 90) + 1) → nquad
  15. If(Mod[nquad, 4] ≟ 0, 4, Mod[nquad, 4]) → quad
  16. Element(ListQuad, quad) → P_q
  17. Polygon(O, P, Q) → poly1, p_x, o, p
  18. Angle(O, Q, P) → rtAngled
  19. Element(ListGenAngle, quad) → P_g
  20. Element(ListRefAngle, quad) → P_f
  21. Midpoint(O, Q) → OQmid
  22. Midpoint(P, Q) → PQmid
  23. Midpoint(O, P) → OPmid
  24. Angle(A, O, P_o) → θ_{c2}
  25. Angle(A, O, P_o) → θ_{c3}
  26. Angle(A, O, P_o) → θ_{c4}
  27. Textfield(θ_o) → inputBox1
  28. If(α_+ ≟ 90° ∨ α_+ ≟ 270°, (θ_r + ((round(θ_r / π, 0) - 1) * π)) / 2, (θ_r + (round(θ_r / π, 0) * π)) / 2) → θ_t
  29. Midpoint(P_{rless20deg}, T_{basicangle}) → T_{genangle}
  30. Segment((x(C) - 0.3, y(C)), (x(A) + 0.3, y(A))) → xaxisline
  31. Mirror(P_{xaxisarrow}, k) → P_{yaxisarrow}
  32. Mirror(xaxisline, k) → yaxisline
  33. If(ReferenceAngle1 < 90.01°, ReferenceAngle1, ReferenceAngle2) → E4
  34. If(ReferenceAngle1 < 90.01°, ReferenceAngle1, ReferenceAngle2) → E5
  35. If(quad ≟ 1, "", If[quad ≟ 4, "", "-"]) → H4
  36. If(quad ≟ 1, "", If[quad ≟ 3, "", "-"]) → H5
  37. If(quad ≟ 1, "positive", If[quad ≟ 2, "positive", "negative"]) → G3
  38. If(quad ≟ 1, "positive", If[quad ≟ 4, "positive", "negative"]) → G4
  39. If(quad ≟ 1, "positive", If[quad ≟ 3, "positive", "negative"]) → G5
  40. If(abs(C3) ≟ 0, 0, If[C3 > 0, If[C3 - (floor(C3 / 360) * 360) ≟ 0, 360, C3 - (floor(C3 / 360) * 360)], If[abs(C3) - (floor(abs(C3) / 360) * 360) ≟ 0, 360, 360 - (abs(C3) - (floor(abs(C3) / 360) * 360))]]) → D3
  41. If(abs(C4) ≟ 0, 0, If[C4 > 0, If[C4 - (floor(C4 / 360) * 360) ≟ 0, 360, C4 - (floor(C4 / 360) * 360)], If[abs(C4) - (floor(abs(C4) / 360) * 360) ≟ 0, 360, 360 - (abs(C4) - (floor(abs(C4) / 360) * 360))]]) → D4
  42. If(abs(C5) ≟ 0, 0, If[C5 > 0, If[C5 - (floor(C5 / 360) * 360) ≟ 0, 360, C5 - (floor(C5 / 360) * 360)], If[abs(C5) - (floor(abs(C5) / 360) * 360) ≟ 0, 360, 360 - (abs(C5) - (floor(abs(C5) / 360) * 360))]]) → D5
  43. Random(1, 3) → selecttrigrationum
  44. If(ReferenceAngle1 < 90.0100000000002°, ReferenceAngle1, ReferenceAngle2) → E1
  45. If(abs(C1) ≟ 0, 0, If[C1 > 0, If[C1 - (floor(C1 / 360) * 360) ≟ 0, 360, C1 - (floor(C1 / 360) * 360)], If[abs(C1) - (floor(abs(C1) / 360) * 360) ≟ 0, 360, 360 - (abs(C1) - (floor(abs(C1) / 360) * 360))]]) → D1
  46. Cell(7, 2 + selecttrigrationum) → G1
  47. If(quad ≟ 1, {J1, K1}, {J1, K1, L1, M1}) → listSelectedTrigChoices
  48. Remove(listSelectedTrigChoices, {txtC1}) → listSelectedTrigChoices2
  49. Remove(listSelectedTrigChoices2, {txtC2}) → listSelectedTrigChoices3
  50. If(quad ≟ 1, {"Select", "a", "b"}, {"Select", "a", "b", "c", "d"}) → listAnswerChoice
  51. IndexOf(Element[listShuffledChoices, SelectedIndex[listAnswerChoice]], listSelectedTrigChoices) → numListFeedback
  52. Textfield(θ_{debug}) → InputBox1