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Unwrapping the Unit Circle

Unwrapping the Unit Circle
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2015-04-17 05:06
CircleAngleVectorTrigonometry
This example demonstrates how to unwrap the unit circle to understand trigonometric functions. It involves key concepts such as the unit circle, angles, and vectors. Using GeoGebra commands like Point, Circle, Intersect, Rotate, etc., it dynamically shows the relationship between angles and trigonometric values. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(yAxis, xAxis) → B
  4. Rotate(B, (-α), A) → B'
  5. Angle(B', A, B) → β
  6. Segment(A, B') → a
  7. Segment(A, B) → b
  8. Segment(B, C) → d
  9. OrthogonalLine(C, xAxis) → e
  10. Circle(C, 1) → f
  11. CircleArc(A, B, B') → p
  12. Intersect(f, e, 2) → D
  13. Circle(D, 1) → g
  14. Rotate(C, (-α), D) → C'
  15. Angle(C', D, C) → γ
  16. Segment(D, C') → i
  17. CircleSector(D, C, C') → h
  18. CircleArc(D, C, C') → k
  19. Midpoint(D, C) → I
  20. Vector(J, K) → u
  21. Vector(L, M) → v