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Quiz on Solving Trig Equations

Quiz on Solving Trig Equations
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2020-12-09 15:20
FunctionTrigonometryGeometric Construction
This example demonstrates how to solve simple trigonometric equations within one revolution using GeoGebra. It involves core math concepts like trigonometric functions, equation solving, unit circle, and angle transformations. Construction highlights include commands and objects such as RandomElement, If, Textfield, Random, Corner, Line, Point, Circle, Rotate, Angle, Ray, Intersect, Segment. Suitable for high school mathematics teaching, reinforcing the solution methods of trigonometric equations through practice and interactive exploration.

GeoGebra Commands & Parameters

  1. RandomElement(listans1) → qdec1
  2. RandomElement(qQlist) → qQ
  3. RandomElement(listans2) → qdec2
  4. RandomElement(listans3) → qdec3
  5. RandomElement(listans4) → qdec4
  6. If(qQ ≟ 1, qdec1, If[qQ ≟ 2, qdec2, If[qQ ≟ 3, qdec3, qdec4]]) → qdec
  7. If((rR ≟ 1 ∨ rR ≟ 3) ∧ qdec ≟ 0, 1, 0) → showbox3
  8. Textfield(stans2) → InputBox2
  9. If(rR ≟ 1 ∧ qdec ≟ 1 ∨ rR ≟ 1 ∧ qdec ≟ -1 ∨ rR ≟ 2 ∧ qdec ≟ -1, 0, 1) → showbox2
  10. If(rR ≟ 1, round(180° - arcs, 1), If[rR ≟ 2, round(360° - arcc, 1), round(180° + arct, 1)]) → aNS2poszero
  11. If(rR ≟ 1, round(360° + arcs, 1), If[rR ≟ 2, round(360° - arcc, 1), round(360° + arct, 1)]) → aNS2neg
  12. Random(1, 3) → rRran3
  13. If(qQ ≟ 1, qdec1, If[qQ ≟ 2, qdec2, If[qQ ≟ 3, qdec3r, qdec4r]]) → qdecr
  14. If(qdecr ≟ 0.87, pr3o2, If[qdecr ≟ -0.87, nr3o2, If[qdecr ≟ 0.71, pr2o2, If[qdecr ≟ -0.71, nr2o2, If[qdecr ≟ 0.58, pr3o3, If[qdecr ≟ -0.58, nr3o3, If[qdecr ≟ 1.73, pr3, If[qdecr ≟ -1.73, nr3, Text[qdecr]]]]]]]]) → thetatext
  15. If(rR ≟ 1, text1, If[rR ≟ 2, text2, text3]) → qtext
  16. If(rR ≟ 1, round(180° - arcs, 1), If[rR ≟ 2, arccr, round(180° + arct, 1)]) → aNS1neg
  17. If(rR ≟ 1, arcsr, If[rR ≟ 2, arccr, arctr]) → aNS1poszero
  18. Textfield(stans1) → InputBox1
  19. Textfield(stans3) → InputBox3
  20. Random(1, 2) → rRran2
  21. If(qdec ≥ 0, Text[aNS1poszero], Text[aNS1neg]) → theta1text
  22. If(showbox2 ≟ 1 ∧ qdec ≥ 0, (", " * Text[aNS2poszero]), If[showbox2 ≟ 1 ∧ qdec < 0, (", " * Text[aNS2neg]), ""]) → theta2text
  23. If(showbox3 ≟ 1, (", " * Text[aNS3]), "") → theta3text
  24. Corner(5) → dims
  25. Line(A, B) → f
  26. Point(f) → C
  27. Circle(C, D) → c
  28. Rotate(B, 25°, C) → B'
  29. Angle(B, C, B') → α
  30. Rotate(A, -25°, C) → A'
  31. Angle(A', C, A) → β
  32. Ray(C, B') → g
  33. Ray(C, A') → h
  34. Intersect(c, h) → E,
  35. Intersect(c, g) → F,
  36. Segment(C, F) → i
  37. Segment(C, E) → j
  38. Segment(A, B) → k

AI Drawing Prompt Reference

Draw a unit circle with center C and radius 1. Draw a ray g from C to the right, intersecting the circle at point F. Draw a ray h from C to the left, intersecting the circle at point E. Connect C and F, and C and E to form chords i and j. Randomly select an angle on the circle, determine the sign of the angle based on the sine value, calculate the corresponding radian value, and find the intersection points E and F on rays g and h. Finally, label the radian value corresponding to the angle on the circle.
The prompt above was compiled from the original drawing commands and is for reference only.