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Interactive Unit Circle by Ms. Kaeli

Interactive Unit Circle by Ms. Kaeli
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2018-08-25 23:25
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between angles and coordinates on the unit circle and the patterns involved. Core math concepts include the unit circle, trigonometric functions, and coordinate geometry. It is constructed using GeoGebra commands like Intersect, Circle, Mirror, Point, Segment, Angle, OrthogonalLine, and Line. Suitable for high school mathematics teaching or self-study to understand the definition of trigonometric functions and properties of the unit circle.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Mirror(B, yAxis) → B'
  4. Mirror(B, xAxis) → B'_1
  5. Mirror(B', xAxis) → B''
  6. Mirror(C, yAxis) → C'
  7. Mirror(C', xAxis) → C''
  8. Mirror(C'', yAxis) → C'''
  9. Mirror(D, yAxis) → D'
  10. Mirror(D', xAxis) → D''
  11. Mirror(D'', yAxis) → D'''
  12. Point(c) → I
  13. Segment(I, A) → g
  14. Angle(E, A, I) → α
  15. OrthogonalLine(I, xAxis) → h
  16. Intersect(h, xAxis) → Q
  17. Line(A, Q) → i
  18. Segment(I, Q) → j
  19. Segment(A, Q) → k