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Trigonometric Unit Circle with Exact Values

Trigonometric Unit Circle with Exact Values
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2018-02-21 00:43
CircleTrigonometryComplex NumberGeometric ConstructionGraphing
This example demonstrates the geometric representation of the trigonometric unit circle and its exact values. It involves core mathematical concepts such as the unit circle, trigonometric functions (sine, cosine), right triangles, complex numbers, exponential functions, and step functions. The construction uses GeoGebra commands like Circle, Line, Segment, Function, Polygon, Angle, Intersect, Tangent, Point, and Dilate to draw the unit circle, angles, trigonometric function graphs, and exact value annotations. It is suitable for high school and above students to understand the relationship between trigonometric functions and the unit circle, as well as the geometric meaning of complex numbers.

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'