Connection Between Right Triangle Trigonometry and Unit Circle

Connection Between Right Triangle Trigonometry and Unit Circle
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2017-01-28 08:12
This example demonstrates the geometric relationship between right triangles and the unit circle, dynamically illustrating the definitions of trigonometric functions. Core math concepts include right triangles, unit circles, sine, cosine, angles, etc. It is constructed using GeoGebra commands like Intersect, Circle, Rotate, OrthogonalLine, Segment, Angle, and Tangent. Suitable for high school mathematics, helping students understand the definitions and properties of trigonometric functions on the unit circle.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, α) → B'
  5. OrthogonalLine(B', xAxis) → f
  6. Intersect(f, xAxis) → C
  7. Segment(A, B') → g
  8. Segment(B', C) → h
  9. Segment(A, C) → i
  10. Angle(B', A, C) → β
  11. Angle(A, C, B') → γ
  12. Tangent(B', c) → j,
  13. Intersect(j, xAxis) → D
  14. Segment(B', D) → k
  15. Intersect(c, xAxis, 2) → E
  16. Segment(A, E) → m
  17. Angle(E, A, B') → δ