Unit Circle Half Angle Diagram

Unit Circle Half Angle Diagram
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2015-05-07 23:36
This example demonstrates the geometric representation of half-angle formulas in the unit circle, dynamically showing the relationship between half-angle trigonometric values and the original angle. Core mathematical concepts include the unit circle, trigonometric functions, half-angle formulas, and complex number representations. Construction highlights involve GeoGebra commands/objects like Intersect, Circle, Point, Vector, Segment, Ray, and Angle. Suitable for high school mathematics education to understand the geometric meaning of trigonometric functions and the application of half-angle formulas.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → d
  3. Point(d) → P
  4. Vector(O, P) → u
  5. Segment(Q, P) → e
  6. Intersect(d, xAxis, 1) → A
  7. Segment(A, P) → a
  8. Intersect(a, yAxis) → B
  9. Ray(A, P) → b
  10. Intersect(d, xAxis, 2) → C
  11. Angle(C, O, P) → θ
  12. Angle(C, A, P) → α