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Define SINE COSINE with the unit-circle

Define SINE COSINE with the unit-circle
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2015-02-09 12:43
CircleTrigonometryCoordinate GeometryGeometric Construction
This example geometrically demonstrates the definitions of sine and cosine using the unit circle. Key math concepts include the unit circle, trigonometric function definitions, and right triangle side length relationships. GeoGebra commands and objects used in the construction are Vector, Translate, Segment, Circle, Point, OrthogonalLine, Line, Intersect, Angle, and CircleArc. It is suitable for high school students learning the geometric meaning of trigonometric functions and for introductory calculus education.

GeoGebra Commands & Parameters

  1. Vector(O, O') → u
  2. Translate(A, Vector[0.1 * u]) → A'
  3. Segment(A, A') → a
  4. Circle(O, 1) → c
  5. Point(c) → M
  6. OrthogonalLine(M, a) → b
  7. Line(M, a) → d
  8. Intersect(d, yAxis) → C
  9. Intersect(b, xAxis) → D
  10. Segment(M, O) → e
  11. Segment(M, D) → f
  12. Segment(M, C) → g
  13. Angle(O', O, M) → α
  14. CircleArc(O, O', O'') → p
  15. Point(p) → P
  16. OrthogonalLine(P, a) → h
  17. Line(P, a) → i
  18. Intersect(i, yAxis) → E
  19. Intersect(h, xAxis) → F
  20. Segment(O, P) → j
  21. Segment(E, P) → k
  22. Segment(F, P) → l
  23. Angle(F, O, P) → β