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Double Angle Formula via Area

Double Angle Formula via Area
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2016-08-27 04:09
FunctionTrigonometryGeometric Construction
This example demonstrates the double angle formula for sine through the area. It involves core trigonometry concepts and uses GeoGebra commands such as rotation, polygon, and intersection to visually illustrate the geometric meaning of the double angle formula. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Point({0, 0}) → A
  2. Point({1, 0}) → B
  3. Rotate(B, a°, A) → D
  4. Segment(C, B) → h
  5. Angle(B, A, D) → α
  6. Polygon({A, B, C, D}) → poly1
  7. Segment(D, B) → f
  8. Segment(A, C) → g
  9. Intersect(f, g) → D_1
  10. Point(h) → E
  11. Polygon({E, G, F}) → poly2
  12. Segment(C, D) → i
  13. Point(i) → H
  14. Angle(E, F, G) → β
  15. Angle(G, E, F) → γ
  16. Polygon(H, I, J) → poly3, j_1, h_2, i_2
  17. Angle(J, H, I) → δ
  18. Angle(I, J, H) → ε