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Unit Circle (Quadrant Identities)

Unit Circle (Quadrant Identities)
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2017-05-22 17:59
CircleTrigonometryGeometric Construction
This example demonstrates quadrant identities on the unit circle. Key mathematical concepts include trigonometry and the unit circle. Using GeoGebra commands such as Intersect, Circle, and Point, the construction of points on the unit circle and related quadrant angles is illustrated. Suitable for high school mathematics education and learning trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Point(c) → C
  4. Point(Circle[A, 1]) → D
  5. Segment(A, C) → f
  6. OrthogonalLine(C, f) → g
  7. Intersect(g, xAxis) → E
  8. Intersect(g, yAxis) → F
  9. OrthogonalLine(C, xAxis) → j
  10. Intersect(j, xAxis) → G
  11. OrthogonalLine(C, yAxis) → k
  12. Intersect(k, yAxis) → H
  13. Segment(A, H) → l
  14. Segment(A, G) → m
  15. Segment(C, G) → q
  16. Segment(C, H) → r
  17. Angle(C, G, A) → β
  18. Angle(B, A, C) → Θ
  19. Intersect(m, q) → J
  20. Polygon(C, J, A) → poly1, a, c_1, j_1
  21. Ray(A, C) → i
  22. Point(yAxis) → I
  23. Point(xAxis) → K
  24. Segment(I, K) → h
  25. OrthogonalLine(K, h) → n
  26. OrthogonalLine(I, h) → p
  27. Intersect(p, xAxis) → L
  28. OrthogonalLine(L, p) → s
  29. Intersect(n, s) → M
  30. Segment(I, L) → t
  31. Segment(L, M) → b
  32. Segment(M, K) → d
  33. Intersect(i, t) → N
  34. Intersect(i, b) → O
  35. Intersect(i, d) → P
  36. Angle(N, A, L) → α
  37. Angle(L, A, O) → γ
  38. OrthogonalLine(N, yAxis) → e
  39. Intersect(e, h) → Q
  40. Segment(A, Q) → f_1
  41. Intersect(c, f_1, 1) → R
  42. Angle(K, A, R) → δ
  43. OrthogonalLine(R, xAxis) → g_1
  44. Intersect(g_1, xAxis) → S
  45. Segment(A, R) → h_1
  46. Segment(R, S) → i_1
  47. Segment(S, A) → k_1
  48. Ray(O, A) → l_1
  49. Intersect(c, l_1, 2) → T
  50. OrthogonalLine(T, xAxis) → m_1
  51. Intersect(m_1, xAxis) → U
  52. Segment(A, T) → n_1
  53. Segment(T, U) → p_1
  54. Segment(U, A) → q_1
  55. Angle(U, A, T) → ε
  56. OrthogonalLine(P, xAxis) → r_1
  57. Intersect(r_1, h) → V
  58. Segment(A, V) → s_1
  59. Intersect(c, s_1, 1) → W
  60. Segment(A, W) → t_1
  61. Segment(W, J) → a_1
  62. Angle(K, A, W) → ζ
  63. Angle(P, A, K) → η
  64. Intersect(i, b) → H_1
  65. Intersect(i, t) → I_1
  66. Intersect(i, h) → J_1