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Demonstrating Sine, Cosine, and Secant on the Unit Circle

Demonstrating Sine, Cosine, and Secant on the Unit Circle
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2020-02-27 11:05
CircleTrigonometryGeometric Construction
This example uses the unit circle to illustrate how the relationship between sine, cosine, and secant varies with changes in the central angle. It covers core trigonometric concepts, geometric constructions using GeoGebra commands like Intersect, Point, Circle, Segment, Angle, Line, and is suitable for high school mathematics education to visually explain the definitions and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → B
  3. Circle(O, B) → g
  4. Point(g) → A
  5. Intersect(g, xAxis, 2) → D
  6. Segment(D, B) → a
  7. Point(g) → P
  8. Intersect(g, yAxis, 2) → C
  9. Segment(A, C) → c
  10. Angle(B, O, P) → θ
  11. Line(B, O) → h
  12. Line(O, P) → l
  13. Line(B, c) → d
  14. Line(P, c) → e
  15. Intersect(l, d) → F_1
  16. Intersect(h, e) → E
  17. Line(D, c) → b
  18. Intersect(l, b) → F_2
  19. Segment(O, E) → cosine
  20. Segment(F_1, O) → secant01
  21. Segment(F_2, O) → secant02
  22. Segment(P, E) → sine