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Sines, Tangents and Secants on a Unit Circle

Sines, Tangents and Secants on a Unit Circle
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2016-09-01 04:38
CircleTrigonometryGeometric Construction
This example illustrates the geometric meanings of sines, tangents, and secants on a unit circle. Using commands like intersection, circle, rotation, angle, ray, and tangent, it provides a visual understanding of trigonometric functions. Suitable for high school mathematics education and learning trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, α, A) → B'
  5. Angle(B, A, B') → β
  6. Ray(A, B') → a
  7. Tangent(B, c) → b,
  8. OrthogonalLine(B', xAxis) → d
  9. OrthogonalLine(B', yAxis) → e
  10. Intersect(e, yAxis) → C
  11. Intersect(d, xAxis) → D
  12. Intersect(b, a) → E
  13. Segment(E, B) → f
  14. Segment(E, A) → g
  15. Segment(B', A) → h
  16. Segment(B', C) → i
  17. Segment(B', D) → j
  18. Angle(B', A, C) → γ
  19. Intersect(c, yAxis, 2) → F
  20. Tangent(F, c) → k,
  21. Intersect(k, a) → G
  22. Segment(F, G) → l
  23. Segment(A, G) → m