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Unit Circle Coordinates

Unit Circle Coordinates
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2016-09-01 04:31
CircleTrigonometryCoordinate Geometry
This example demonstrates coordinates on the unit circle. Core mathematical concepts include trigonometry and coordinate geometry. Using GeoGebra commands such as Intersect, Circle, Rotate, etc., it dynamically shows the coordinate changes of points on the unit circle. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Intersect(c, yAxis, 2) → C
  5. Intersect(c, xAxis, 1) → D
  6. Intersect(c, yAxis, 1) → E
  7. Rotate(B, 30°, A) → B'
  8. Angle(B, A, B') → α
  9. Rotate(B, 45°, A) → B'_1
  10. Angle(B, A, B'_1) → β
  11. Rotate(B, 60°, A) → B'_2
  12. Angle(B, A, B'_2) → γ
  13. Mirror(B'_2, xAxis) → F
  14. Mirror(B'_1, xAxis) → G
  15. Mirror(B', xAxis) → B''
  16. Mirror(B'_2, yAxis) → H
  17. Mirror(B'_1, yAxis) → I
  18. Mirror(B', yAxis) → B''_1
  19. Mirror(H, xAxis) → H'
  20. Mirror(I, xAxis) → I'
  21. Mirror(B''_1, xAxis) → J
  22. Segment(B'_2, H') → f
  23. Segment(J, B') → g
  24. Segment(B'_1, I') → h
  25. Segment(H, F) → i
  26. Segment(I, G) → j
  27. Segment(B''_1, B'') → k