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Unit Circle by ryanjendrek

Unit Circle by ryanjendrek
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2015-03-26 07:23
CircleTrigonometryCoordinate GeometryGeometric Construction
In collections The Unit Circle Begins
This example demonstrates the construction of the unit circle and its relationship with trigonometric functions. Key mathematical concepts include the definition of the unit circle, trigonometric values, and the conversion between angles and radians. Construction highlights involve using GeoGebra commands such as Intersect, Circle, Point, Segment, OrthogonalLine, Angle, Mirror, and Rotate to build the unit circle and related geometric elements. Suitable for high school students learning trigonometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Segment(A, B) → a
  5. OrthogonalLine(B, xAxis) → b
  6. Angle(xAxis, a) → Θ_1
  7. Intersect(c, a) → D,
  8. Point(c) → F
  9. Point(c) → G
  10. Mirror(H, yAxis) → H'
  11. Mirror(H', xAxis) → H''
  12. Mirror(H'', yAxis) → H'''
  13. Mirror(I, yAxis) → I'
  14. Mirror(I', xAxis) → I''
  15. Mirror(I'', yAxis) → I'''
  16. Mirror(J, yAxis) → J'
  17. Mirror(J', xAxis) → J''
  18. Mirror(J'', yAxis) → J'''
  19. Intersect(c, xAxis, 2) → E
  20. Rotate(E, Θ_2, A) → E'_1
  21. Angle(E, A, E'_1) → Θ
  22. Segment(A, E'_1) → d
  23. OrthogonalLine(E'_1, xAxis) → e
  24. Intersect(e, xAxis) → C
  25. Segment(E'_1, C) → f
  26. Segment(A, C) → g
  27. Segment(A, C) → h