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Trigonometric Unit Circle Demo

Trigonometric Unit Circle Demo
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2017-10-06 17:19
CircleAngleVectorFunctionTrigonometry
This example visually demonstrates the relationship between trigonometric functions and the unit circle, illustrating concepts like angles, sine, cosine, and tangent. It involves core mathematical ideas such as the unit circle, trigonometric ratios, and symmetry. The construction uses GeoGebra commands/objects like Circle, Point, OrthogonalLine, Segment, Intersect, Tangent, Angle, Polygon, Vector, and Translate. Suitable for high school mathematics education to help students intuitively understand the definitions and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → P
  3. OrthogonalLine(A, yAxis) → a
  4. OrthogonalLine(P, a) → b
  5. OrthogonalLine(P, yAxis) → d
  6. Segment(A, P) → e
  7. Intersect(yAxis, d) → C
  8. Intersect(b, a) → D
  9. Segment(P, C) → cosθ
  10. Segment(D, P) → sinθ
  11. Tangent(P, c) → h,
  12. Intersect(yAxis, h) → E
  13. Intersect(a, h) → F
  14. Segment(F, A) → secθ
  15. Segment(A, E) → cscθ
  16. Segment(P, E) → cotθ
  17. Segment(P, F) → tanθ
  18. Angle(P, A, B) → θ
  19. Polygon(P, A, D) → poly1, d_1, p, a_1
  20. Vector(A, G) → u
  21. Translate(P, u) → P'
  22. Translate(A, u) → A'
  23. Translate(D, u) → D'
  24. Polygon(P', A', D') → poly1', d', cosθ_1, sinθ_1
  25. Angle(P', A', D') → θ_1