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Trigonometric Equations Demo

Trigonometric Equations Demo
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2016-02-15 19:53
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example dynamically demonstrates trigonometric equations by visualizing points, arcs, and trigonometric lines on the unit circle, providing an intuitive understanding of the solutions. It involves core concepts like trigonometric functions, unit circle, cosine law, sine law, and angle calculations. The construction uses GeoGebra commands: Circle, Segment, Arc, If, Textfield. Suitable for high school and above students to grasp the geometric meaning and solving methods of trigonometric equations.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → d
  2. Segment(P, Pc) → segmcos
  3. Segment(P, Ps) → segmsin
  4. Segment((0, 0), P) → radP
  5. Segment((0, 0), Pc) → radPc
  6. Segment((0, 0), Ps) → radPs
  7. Circle((0, 0), 0.8) → e
  8. Arc(e, (0, 0), P) → arcPabove
  9. Circle((0, 0), 0.7) → f
  10. Arc(f, (0, 0), Ps) → arcPsabove
  11. Arc(e, P, (0, 0)) → arcPbelow
  12. Arc(f, Pc, (0, 0)) → arcPcabove
  13. Arc(f, Ps, (0, 0)) → arcPsbelow
  14. Arc(f, (0, 0), Pc) → arcPcbelow
  15. If(s ≥ 0, acos(c), (-acos(c))) → angleP
  16. If(s < 0, acos(c), (-acos(c))) → anglePc
  17. If(s ≥ 0, acos((-c)), (-acos((-c)))) → anglePs
  18. Textfield(c) → InputBox1
  19. Textfield(s) → InputBox2