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Unit Circle Exploration by Alfonso Garcia

Unit Circle Exploration by Alfonso Garcia
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2018-05-16 00:31
CircleTrigonometryGeometric Construction
This example demonstrates points on the unit circle and related geometric elements. Key mathematical concepts include the unit circle, angles, and tangents. Using GeoGebra commands such as rotation, angle measurement, and line segment construction, it shows how points on the unit circle move with changes in angle. Suitable for high school mathematics education, particularly in trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis) → C, D
  4. Rotate(D, α, A) → D'
  5. Angle(D, A, D') → β
  6. Segment(A, D') → a
  7. Angle(D', A, C) → γ
  8. Angle(D', A, D) → δ
  9. OrthogonalLine(D', xAxis) → b
  10. Intersect(b, xAxis) → F
  11. Segment(D', F) → d
  12. Segment(E, F) → e
  13. Text(θ) → text1
  14. Text(x(D')) → cosβ
  15. Text(y(D')) → text4
  16. FractionText(θ) → text5
  17. Angle(D', E, F) → ε