MathPlotAI Logo MathPlotAI

Geometric Construction of Sine and Cosine for 30n° Angles

Geometric Construction of Sine and Cosine for 30n° Angles
Loading the math board and drawing, please wait…
2016-10-01 12:41
AngleFunctionTrigonometryGeometric Construction
This example demonstrates the geometric representation of sine and cosine values for angles that are integer multiples of 30 degrees. Key concepts include trigonometric functions, unit circle properties, and sequence patterns. Construction utilizes GeoGebra commands such as Circle, Mirror, Segment, Polygon, and Angle to visualize the relationships. It is designed for high school students learning trigonometry or educators creating dynamic classroom demonstrations to illustrate special angle values and periodicity.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Intersect(c, f, 1) → C
  5. Intersect(c, f, 2) → D
  6. Intersect(c, g, 2) → E
  7. Intersect(c, g, 1) → F
  8. Mirror(E, xAxis) → E'
  9. Mirror(F, xAxis) → F'
  10. Mirror(C, yAxis) → C'
  11. Mirror(D, yAxis) → D'
  12. Intersect(c, xAxis, 2) → G
  13. Intersect(c, yAxis, 2) → H
  14. Intersect(c, yAxis, 1) → I
  15. Segment(A, E) → j
  16. Segment(A, E') → k
  17. Segment(E, E') → l
  18. Polygon(A, C', C) → poly2, n, p, q
  19. Polygon(A, E', E) → poly1, e, a, e'
  20. Segment(G, C') → m
  21. Polygon(A, F, F') → poly4, f', a_3, f_1
  22. Polygon(D, D', A) → poly5, r, s, t
  23. Segment(A, B) → b
  24. Segment(A, H) → d
  25. Segment(G, A) → g_1
  26. Segment(A, I) → h_1
  27. Intersect(i, l) → J
  28. Segment(A, J) → i_1
  29. Angle(E, J, A) → α
  30. Intersect(h, p) → K
  31. Segment(K, A) → j_1
  32. Angle(C', K, A) → β
  33. Intersect(i, a_3) → L
  34. Segment(L, A) → k_1
  35. Angle(F', L, A) → γ
  36. Intersect(h, r) → M
  37. Segment(A, M) → l_1
  38. Angle(D, M, A) → δ
  39. Polygon(P, N, O, Q) → poly3, p_1, n_1, o, q_1
  40. Polygon(P_1, N_1, O_1, Q_1) → poly3_1, p_2, n_2, o_1, q_2
  41. Polygon(P_2, N_2, O_2, Q_2) → poly3_2, p_3, n_3, o_2, q_3
  42. Polygon(P_3, N_3, O_3, Q_3) → poly3_3, p_4, n_4, o_3, q_4
  43. Polygon(P_4, N_4, O_4, Q_4) → poly3_4, p_5, n_5, o_4, q_5
  44. Polygon(P_5, N_5, O_5, Q_5) → poly3_5, p_6, n_6, o_5, q_6
  45. Polygon(P_6, N_6, O_6, Q_6) → poly3_6, p_7, n_7, o_6, q_7
  46. Polygon(P_7, N_7, O_7, Q_7) → poly3_7, p_8, n_8, o_7, q_8
  47. Polygon(P_8, N_8, O_8, Q_8) → poly3_8, p_9, n_9, o_8, q_9
  48. Polygon(P_9, N_9, O_9, Q_9) → poly3_9, p_{10}, n_{10}, o_9, q_{10}
  49. Polygon(P_{10}, N_{10}, O_{10}, Q_{10}) → poly3_{10}, p_{11}, n_{11}, o_{10}, q_{11}
  50. Polygon(P_{11}, N_{11}, O_{11}, Q_{11}) → poly3_{11}, p_{12}, n_{12}, o_{11}, q_{12}