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Determining Exact Values of Trig Ratios

Determining Exact Values of Trig Ratios
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2018-01-19 04:46
CircleAngleTrigonometryGeometric Construction
This example demonstrates how to geometrically construct and determine exact values of trigonometric ratios. Key math concepts include trigonometry, equilateral triangles, circles, and angle measurement. GeoGebra commands used in the construction are: Intersect, Point, Circle, Segment, Distance, Angle, Vector, Polygon, Line, and Mirror. Suitable for high school mathematics education to help students understand the geometric meaning and calculation of trigonometric values.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → E
  3. Circle(O, E) → c_1
  4. Point(c_1) → P
  5. Segment(O, P) → a
  6. Distance(P, A_1) → b
  7. Angle(E, O, P) → α
  8. Segment(A_1, (x(A_1), 0)) → f
  9. Segment(A_2, (x(A_2), 0)) → g
  10. Segment(B_2, B_1) → h
  11. Segment(C_2, C_1) → i
  12. Vector(O, P) → u
  13. Vector(P, (x(P), 0)) → v
  14. Vector(P, (0, y(P))) → w
  15. Point(u) → A
  16. Segment(A, C_2) → e
  17. Segment(A, B_2) → j
  18. Segment(A, A_2) → k
  19. Segment(A, A_3) → l
  20. Segment(A, B_3) → m
  21. Segment(A, C_3) → n
  22. Segment(A, C_4) → p
  23. Segment(A, B_4) → q
  24. Segment(A, A_4) → r
  25. Segment(A, A_1) → s_1
  26. Segment(A, B_1) → t
  27. Segment(A, C_1) → a_1
  28. Polygon(P, (x(P), 0), A) → poly1, a_2, B, b_1
  29. Polygon((abs(x(P)), abs(y(P))), A, (abs(x(P)), 0)) → poly2, d_1, e_1, a_3
  30. Point(d_1) → C
  31. Line(C, C_1) → s
  32. Point(e) → D
  33. Line(C, D) → c
  34. Point(j) → F
  35. Line(C, F) → f_1
  36. Point(k) → G
  37. Line(C, G) → g_1
  38. Point(l) → H
  39. Line(C, H) → h_1
  40. Point(m) → I
  41. Line(C, I) → i_1
  42. Intersect(c_1, c) → J, K
  43. Intersect(c_1, f_1) → L, M
  44. Intersect(c_1, h_1) → R, T
  45. Intersect(c_1, i_1) → U, V
  46. Intersect(c_1, s) → Z, D_1
  47. Segment(M, L) → l_1
  48. Segment(V, U) → m_1
  49. Segment(D_1, Z) → n_1
  50. Segment(K, J) → p_1
  51. Segment(T, R) → k_1
  52. Mirror(R, xAxis) → R'
  53. Point(l_1) → Q
  54. Line(R', Q) → j_1
  55. Intersect(c_1, j_1) → E_1, F_1
  56. Segment(F_1, E_1) → q_1