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Exploring the Unit Circle by Andrew Gandert

Exploring the Unit Circle by Andrew Gandert
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2016-09-26 23:29
CircleTrigonometry
This example demonstrates the basic properties of the unit circle through rotation and intersection operations. Key mathematical concepts include circle, unit circle, angle, and vector. Using GeoGebra commands such as Intersect, Rotate, Segment, etc., the relationship between points on the unit circle and angles can be visually demonstrated. Suitable for students at the junior high school level and above to learn geometric construction and trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, list1(n), A) → B'
  5. Segment(A, B') → f
  6. Line(A, B) → g
  7. OrthogonalLine(B', g) → h
  8. Intersect(g, h) → C
  9. Segment(B', C) → i
  10. Segment(A, C) → j
  11. SurdText(j) → text2
  12. Midpoint(A, C) → D
  13. SurdText(i) → text3
  14. Midpoint(C, B') → E
  15. SurdText(y(B')) → text8
  16. SurdText(x(B')) → text9
  17. Angle(B, A, B') → α
  18. Text(α) → text11
  19. SurdText(B') → text12
  20. SurdText(y(B') / x(B')) → text10