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Six Basic Trigonometric Functions on the Unit Circle

Six Basic Trigonometric Functions on the Unit Circle
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2016-01-09 04:44
CircleFunctionTrigonometry
This example demonstrates the geometric relationships between the six basic trigonometric functions on the unit circle. It involves key mathematical concepts such as trigonometry, unit circle, and geometric transformations. Using GeoGebra commands like Point, Intersect, Segment, etc., the geometric representations of these trigonometric functions can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Intersect(xAxis, yAxis) → B
  3. Segment(B, A) → a
  4. Intersect(c, xAxis, 2) → C
  5. OrthogonalLine(C, xAxis) → b
  6. OrthogonalLine(A, xAxis) → d
  7. Intersect(d, xAxis) → D
  8. Ray(B, A) → e
  9. Intersect(b, e) → E
  10. Segment(B, E) → f
  11. Segment(A, D) → g
  12. Segment(D, B) → h
  13. OrthogonalLine(E, b) → i
  14. OrthogonalLine(A, g) → j
  15. Intersect(j, yAxis) → G
  16. Intersect(i, yAxis) → H
  17. OrthogonalLine(A, a) → k
  18. Intersect(k, xAxis) → I
  19. Intersect(k, yAxis) → J
  20. Segment(H, E) → l
  21. Segment(G, A) → m
  22. Segment(B, G) → n
  23. Segment(B, H) → p
  24. Segment(B, J) → q
  25. Segment(B, C) → r
  26. Segment(B, I) → s
  27. Angle(C, B, A) → θ
  28. Segment(C, E) → t
  29. Intersect(c, q, 1) → K
  30. OrthogonalLine(K, q) → a_1
  31. Intersect(a_1, e) → L
  32. Segment(B, L) → b_1
  33. Segment(J, I) → c_1
  34. Segment(K, L) → d_1
  35. Segment(A, I) → g_1
  36. Segment(A, J) → h_1