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Reference Angle in the First Quadrant

Reference Angle in the First Quadrant
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2019-03-26 17:39
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the construction and properties of reference angles in the first quadrant. It involves core math concepts like trigonometric functions, right triangles, and coordinate geometry. GeoGebra commands used include CurveCartesian for curves, Point for marking points, Mirror for reflection, Segment for lines, Angle for measuring angles, OrthogonalLine for perpendicular lines, and Intersect for finding intersections. Suitable for high school mathematics education, illustrating the application of trigonometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), sin(t), t, 0, (2 * π)) → a
  2. Point(a) → A
  3. Mirror(A, yAxis) → A'
  4. Mirror(P, yAxis) → P_2
  5. Segment(C, P) → f
  6. Angle(B, C, P) → α_1
  7. Mirror(P, xAxis) → P4
  8. Point(f) → E
  9. Segment(E, P_2) → g
  10. Segment(E, P3) → h
  11. Segment(E, P4) → i
  12. Angle(B, E, P_2) → γ
  13. Angle(B, E, P3) → δ
  14. Angle(B, E, P4) → ε
  15. OrthogonalLine(P, xAxis) → j
  16. Intersect(j, xAxis) → D
  17. Segment(P, D) → k
  18. OrthogonalLine(P_2, xAxis) → l
  19. Intersect(l, xAxis) → F
  20. Segment(F, P_2) → m
  21. Segment(E, F) → n
  22. Intersect(n, xAxis) → G
  23. Segment(P3, F) → p
  24. Segment(E, F) → q
  25. Segment(P4, D) → r
  26. Segment(E, D) → s
  27. Intersect(k, xAxis) → H
  28. Point(h) → I
  29. Segment(H, I) → t
  30. Angle(P, E, D) → β
  31. Angle(D, E, P) → ζ
  32. Angle(P, E, D) → η