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Practice Quiz: Trig Equations One Rotation

Practice Quiz: Trig Equations One Rotation
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2020-12-04 17:07
CircleFunctionTrigonometryInequalityGraphing
① This interactive quiz demonstrates solving simple trigonometric equations within one full rotation (0 to 2π) on the unit circle, with students entering answers and receiving immediate feedback. ② Core math concepts include trigonometric equations, the unit circle, properties of sine, cosine, and tangent, periodicity, and solution sets over a specified interval. ③ Construction highlights: uses RandomElement and Random to generate random questions, If and Textfield for conditional logic and input fields, Corner for layout positioning; key objects include qQlist (question list), stans (standard answers), listans (answer lists), qdec (question description), showbox (display boxes), InputBox, arct/arcs/arcc (inverse trig functions), aNS2poszero/aNS2neg (positive/negative solution checks), and thetatext (angle text) to enable dynamic question generation, input validation, and answer display. ④ Suitable for high school or pre-university students learning trigonometric equations, and useful for teachers in classroom demonstrations or for self-paced practice to reinforce unit circle and equation-solving skills.

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

AI Drawing Prompt Reference

Create an interactive-style unit-circle diagram for a trig-equation practice over one full rotation (0 to 2π). Include angle text placed around the circle and text prompts indicating the solution-set type. Provide visible answer input fields for students to enter their angles (in degrees), and show standard-answer text that changes with the case: a positive or negative solution list depending on the selected equation form. Arrange the layout with dedicated display boxes/prompt areas, then add the corresponding inverse-trig-based angle labels (with appropriate parentheses and sign wording) and the input boxes in a clear corner-based layout.
The prompt above was compiled from the original drawing commands and is for reference only.