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Unit Circle and Trigonometric Functions by Isaac Goh

Unit Circle and Trigonometric Functions by Isaac Goh
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2016-10-19 15:10
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the unit circle and trigonometric functions (sine, cosine, tangent, etc.) by dynamically showing the change of angle and function values. Core math concepts include the unit circle, trigonometric function definitions, angle measurement, and trigonometric identities. Construction highlights GeoGebra commands like Intersect, Circle, Point, Angle, If, Line, Segment, Rotate, and Distance. Suitable for high school students learning trigonometry and analytical geometry, or university foundational mathematics teaching.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, r) → c
  3. Point(c) → B
  4. Angle(Q, A, B) → α
  5. If(test > 180°, true, false) → test2
  6. If(snap, 2°, 0°) → tolerance
  7. If(test2, 360° - test, test) → test3
  8. If(test3 ≤ tolerance, (15 * round(α / 15)), α) → θ'
  9. Line(B', A) → h
  10. Intersect(d, h) → C
  11. Intersect(a, h) → D
  12. Intersect(e, h) → E
  13. Intersect(b, h) → F
  14. Segment(B', P) → sinθ
  15. Segment(P, A) → cosθ
  16. Segment(C, Q) → tanθ
  17. Segment(D, R) → cotθ
  18. Segment(S, E) → m
  19. Segment(T, F) → n
  20. Segment(A, C) → secθ
  21. Angle(Q, A, B') → θ
  22. Segment(A, D) → cscθ
  23. Rotate(Q, 60°) → I
  24. Distance(I, A) → IA
  25. If(IsInteger[θ / (15°)], FractionText[θ / (180°)], 0) → θnum
  26. If(Defined[tanθ], Text[y(B') / x(B')], "Undefined") → textTan
  27. If(Defined[cotθ], Text[x(B') / y(B')], "Undefined") → textCot
  28. If(Defined[secθ], Text[r / x(B')], "Undefined") → textSec
  29. If(Defined[cscθ], Text[r / y(B')], "Undefined") → textCsc
  30. Rotate(Q, 30°) → G
  31. Rotate(Q, 45°) → H
  32. Rotate(Q, 135°) → K
  33. Rotate(Q, 120°) → J
  34. Rotate(Q, 150°) → L
  35. Rotate(Q, 225°) → N
  36. Rotate(Q, 210°) → M
  37. Rotate(Q, 240°) → O
  38. Rotate(Q, 315°) → V
  39. Rotate(Q, 300°) → U
  40. Rotate(Q, 330°) → W