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Trigonometric Ratios of General Angles Self Assessment

Trigonometric Ratios of General Angles Self Assessment
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2017-02-10 18:17
AngleFunctionTrigonometry
In collections Self Assessment MCQs Collection
This example demonstrates the calculation and visualization of trigonometric ratios for any angle, focusing on general angles greater than 360 degrees. It involves core concepts like reference angles and trigonometric functions, constructed using GeoGebra commands such as Intersect, Angle, and Segment. Ideal for high school mathematics education and self-study.

GeoGebra Commands & Parameters

  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