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Unit Circle & Trigonometric Ratios

Unit Circle & Trigonometric Ratios
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2017-02-18 23:21
CircleAngleTrigonometryGeometric Construction
This example demonstrates the geometric relationship between any point on the unit circle and trigonometric ratios (sine, cosine, tangent). It involves core concepts like the unit circle, trigonometric ratios, angles, and right triangles. Construction highlights include using GeoGebra commands such as Circle, Point, Line, OrthogonalLine, Rotate, Angle, Segment, and Intersect. Suitable for high school students learning the definition and geometric meaning of trigonometric functions.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Point(c) → A
  3. Line(O, A) → a_1
  4. OrthogonalLine(O, a_1) → b
  5. Rotate(A, 30°, O) → B
  6. Angle(A, O, B) → α
  7. Rotate(B, 30°, O) → C
  8. Angle(B, O, C) → β
  9. Rotate(C, 30°, O) → D
  10. Angle(C, O, D) → γ
  11. Rotate(D, 30°, O) → E
  12. Angle(D, O, E) → δ
  13. Rotate(E, 30°, O) → F
  14. Angle(E, O, F) → ε
  15. Rotate(F, 30°, O) → G
  16. Angle(F, O, G) → ζ
  17. Rotate(G, 30°, O) → H
  18. Angle(G, O, H) → η
  19. Rotate(H, 30°, O) → I
  20. Angle(H, O, I) → θ_1
  21. Rotate(I, 30°, O) → J
  22. Angle(I, O, J) → ι
  23. Rotate(J, 30°, O) → K
  24. Angle(J, O, K) → κ
  25. Rotate(K, 30°, O) → L
  26. Angle(K, O, L) → λ
  27. Line(O, B) → d
  28. Line(O, A) → e
  29. Line(O, D) → g
  30. Line(O, E) → h
  31. Line(F, O) → i
  32. Circle(O, 5.5) → k
  33. Rotate(A, 45°, O) → A'
  34. Angle(A, O, A') → μ
  35. Rotate(A, 135°, O) → A'_1
  36. Angle(A, O, A'_1) → ν
  37. Rotate(A, 225°, O) → A'_2
  38. Angle(A, O, A'_2) → ξ
  39. Rotate(A, 315°, O) → A'_3
  40. Angle(A, O, A'_3) → ο
  41. Point(c) → M
  42. Segment(O, M) → j
  43. Angle(A, O, M) → theta
  44. Intersect(c, j, 1) → P
  45. OrthogonalLine(M, xAxis) → l
  46. Intersect(l, xAxis) → Q
  47. Segment(M, Q) → p
  48. Segment(O, Q) → m
  49. Segment(M, Q) → q