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Trigonometric Functions on the Unit Circle with Exact Values

Trigonometric Functions on the Unit Circle with Exact Values
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2014-06-11 19:34
CircleFunctionTrigonometry
This example demonstrates the trigonometric values on the unit circle, including sine, cosine, and tangent. It involves the core mathematical concepts of trigonometric functions and their representation on the unit circle. Using GeoGebra commands such as Circle, Line, Segment, and Function, it dynamically shows the values of these functions. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(D, T) → c
  2. Line(A, F) → b
  3. Line(C, E) → d
  4. Segment(D, A) → e
  5. Segment(D, C) → g
  6. Function(sin(x), 0, 6.283185307179586) → h
  7. Function(cos(x), 0, 6.283185307179586) → p
  8. Segment(N, A) → i
  9. Segment(M, C) → j
  10. Segment(M, D) → l
  11. Segment(D, N) → m
  12. Polygon(D, M, C) → poly1, c_1, d_1, m_1
  13. Polygon(D, A, N) → poly2, n, d_2, a_1
  14. Angle(M, D, C) → α
  15. Angle(C, M, D) → β
  16. Angle(A, D, N) → γ
  17. Angle(D, N, A) → δ
  18. Line(E, F) → q
  19. Intersect(c, xAxis, 2) → O
  20. Tangent(O, c) → r,
  21. Line(D, C) → s
  22. Intersect(r, s) → P
  23. Function(tan(x), 0, 6.283185307179586) → t
  24. Point(s) → Q
  25. Polygon(P, O, Q) → poly3, q_1, p_1, o
  26. Angle(P, O, Q) → ε
  27. Line(P, A_1) → b_1
  28. Angle(P, Q, O) → ζ
  29. Angle(N, A, Q) → η
  30. Dilate(pic1, z, B) → pic1'