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Unit Circle by Loizos Loizou

Unit Circle by Loizos Loizou
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2018-02-02 01:14
CircleTrigonometryGeometric Construction
This example demonstrates the properties of the unit circle. Key mathematical concepts include trigonometric functions and angles. It is constructed using commands like rotation and tangent. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Point(xAxis) → B_1
  3. Circle(A_1, B_1) → c
  4. Rotate(B_1, α, A_1) → A
  5. Angle(B_1, A_1, A) → θ
  6. OrthogonalLine(A, xAxis) → a
  7. OrthogonalLine(A, yAxis) → b
  8. OrthogonalLine(B_1, xAxis) → d
  9. Line(A_1, A) → e
  10. Intersect(yAxis, b) → H
  11. Intersect(a, xAxis) → B
  12. Segment(A, H) → f
  13. Segment(A_1, B) → g
  14. Segment(H, A_1) → h
  15. Segment(A, B) → i
  16. Intersect(c, yAxis) → E, F
  17. OrthogonalLine(F, yAxis) → j
  18. Intersect(d, e) → Γ
  19. Intersect(e, j) → Δ
  20. Segment(F, Δ) → k
  21. Segment(B_1, Γ) → l
  22. Tangent(A, c) → m,
  23. Intersect(m, xAxis) → T
  24. Intersect(yAxis, m) → Σ
  25. Segment(A_1, T) → n
  26. Segment(A_1, T) → p
  27. Segment(A_1, Σ) → q
  28. Segment(A_1, B) → r
  29. If(sin(θ) ≤ 0, 1, 0) → red
  30. If(sin(θ) > 0, 1, 0) → ble
  31. Segment(A_1, A) → s
  32. If(cos(θ) ≤ 0, 1, 0) → redcos
  33. If(redcos > 0, 0, 1) → blecos
  34. If(tan(θ) ≤ 0, 1, 0) → redtan
  35. If(redtan > 0, 0, 1) → bletan
  36. Segment(Σ, T) → t
  37. Line(F, E) → a_1
  38. Line(A_1, B_1) → b_1