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Unit Circle: Sine and Cosine Functions

Unit Circle: Sine and Cosine Functions
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2017-06-15 02:30
CircleFunctionTrigonometry
This example demonstrates sine and cosine functions using a unit circle. Key mathematical concepts include trigonometry and the unit circle. It utilizes commands such as Circle, Rotate, Angle, OrthogonalLine, and Vector in GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Rotate(B, Angle, A) → C
  5. Angle(B, A, C) → α
  6. OrthogonalLine(C, xAxis) → f
  7. OrthogonalLine(C, yAxis) → g
  8. Vector(A, C) → u
  9. Intersect(f, xAxis) → D
  10. Intersect(g, yAxis) → E
  11. Intersect(c, yAxis, 2) → F
  12. Intersect(c, xAxis, 2) → G
  13. Intersect(c, yAxis, 1) → H
  14. OrthogonalLine(P_{1}, xAxis) → h
  15. OrthogonalLine(P_{2}, xAxis) → i
  16. OrthogonalLine(P_{3}, xAxis) → j
  17. OrthogonalLine(Q_{2}, xAxis) → k
  18. OrthogonalLine(Q_{1}, xAxis) → l
  19. OrthogonalLine(Q_{3}, xAxis) → m
  20. Intersect(m, xAxis) → I
  21. Intersect(k, xAxis) → K
  22. Intersect(c, xAxis, 2) → L
  23. Intersect(l, xAxis) → J
  24. Intersect(j, xAxis) → M
  25. Intersect(i, xAxis) → N
  26. Intersect(h, xAxis) → O
  27. Polygon(A, P_{1}, O) → poly1, o, a, p_6
  28. Intersect(o, p_6) → P
  29. Polygon(P, P_{2}, N) → poly2, n, p, p_{2}
  30. Polygon(P, P_{3}, M) → poly3, m_1, p_{3}, p_4
  31. Polygon(P, D, C) → poly4, c_1, p_5, d
  32. Vector(C, D) → v
  33. Vector(C, E) → w
  34. Vector(P, C) → b
  35. Segment(F, H) → q
  36. Segment(L, B) → r
  37. Segment(P, Q_{1}) → s
  38. Segment(P, Q_{2}) → t
  39. Segment(P, Q_{3}) → e
  40. Segment(P, R_{1}) → f_1
  41. Segment(P, R_{2}) → g_1
  42. Segment(P, R_{3}) → h_1
  43. Segment(P, S_{1}) → i_1
  44. Segment(P, S_{2}) → j_1
  45. Segment(P, S_{3}) → k_1
  46. Segment(P, P_{1}) → l_1
  47. Segment(P, P_{2}) → n_1
  48. Segment(P, P_{3}) → p_1