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Unit Circle and 6 Trigonometry Ratios

Unit Circle and 6 Trigonometry Ratios
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2016-05-18 08:12
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example dynamically demonstrates the geometric relationship between an angle θ and the values of six trigonometric functions (sine, cosine, tangent, etc.) on the unit circle. It covers core concepts like the unit circle, trigonometric definitions, and right triangle side ratios. Key GeoGebra commands used include Point, Line, Circle, Tangent, and Slider to visualize the functions dynamically. Suitable for high school mathematics education to intuitively understand trigonometric definitions and properties.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Point(yAxis) → C
  3. Point(yAxis) → D
  4. Line(D, C) → Yaxis
  5. Line(D, B) → Xaxis
  6. OrthogonalLine(A, Xaxis) → XequalsCosine_1
  7. Intersect(Xaxis, XequalsCosine_1) → XequalsCosine
  8. Circle(D, B) → UnitCircle
  9. Tangent(A, UnitCircle) → TangentToA,
  10. Intersect(Yaxis, TangentToA) → YequalsCosecant
  11. Intersect(Xaxis, TangentToA) → XequalsSecant
  12. Segment(D, A) → f
  13. Segment(D, XequalsCosine) → Cosineθ
  14. Segment(XequalsCosine, A) → Sineθ
  15. Segment(A, XequalsSecant) → Tangentθ
  16. Segment(A, YequalsCosecant) → Cotangentθ
  17. Segment(D, YequalsCosecant) → Cosecantθ
  18. Segment(D, XequalsSecant) → Secantθ
  19. OrthogonalLine(A, Sineθ) → YequalsSine
  20. Point(YequalsSine) → H
  21. OrthogonalLine(yequalsx, xAxis) → xequalsθ
  22. Intersect(YequalsSine, xequalsθ) → DerivedSine
  23. Intersect(TangentToA, yAxis) → YequalsCosecant2
  24. OrthogonalLine(YequalsCosecant2, yAxis) → YequalsCosecant_1
  25. Intersect(xequalsθ, YequalsCosecant_1) → DerivedCosecant
  26. OrthogonalLine(yequalsx, xequalsθ) → yequalsθ
  27. Intersect(XequalsCosine_1, yequalsθ) → SidewaysCosine
  28. Intersect(f, Cosineθ) → L
  29. Line(L, yequalsx) → YequalsX
  30. OrthogonalLine(SidewaysCosine, YequalsX) → ReflectsSidewaysCosine
  31. Intersect(xequalsθ, ReflectsSidewaysCosine) → DerivedCosine
  32. OrthogonalLine(XequalsSecant, yequalsθ) → XequalsSecant_1
  33. Intersect(yequalsθ, XequalsSecant_1) → SidewaysSecant
  34. OrthogonalLine(SidewaysSecant, YequalsX) → ReflectsSidewaysSecant
  35. Intersect(xequalsθ, ReflectsSidewaysSecant) → DerivedSecant
  36. OrthogonalLine(B, Secantθ) → Xequals1
  37. Line(D, A) → a
  38. Intersect(Xequals1, a) → YequalsTangent
  39. OrthogonalLine(YequalsTangent, Xequals1) → YequalsTangent_1
  40. Intersect(xequalsθ, YequalsTangent_1) → DerivedTangent
  41. OrthogonalLine(C, Cosecantθ) → Yequals1
  42. Intersect(a, Yequals1) → XequalsCotangent_1
  43. OrthogonalLine(XequalsCotangent_1, Yequals1) → XequalsCotangent
  44. Intersect(yequalsθ, XequalsCotangent) → SidewaysCotangent
  45. OrthogonalLine(SidewaysCotangent, YequalsX) → ReflectsSidewaysCotangent
  46. Intersect(xequalsθ, ReflectsSidewaysCotangent) → DerivedCotangent