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Sine and Cosine Components by yvonnemosco

Sine and Cosine Components by yvonnemosco
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2014-12-13 23:49
CircleVectorTrigonometryGeometric Construction
This example illustrates how sine and cosine of angles match as components within a circle, covering core math concepts like trigonometry, circle, vectors, and coordinate geometry. It is constructed using commands like Circle, Point, Angle, Segment, Ray, Intersect, and is suitable for high school and above to understand the geometric meaning of trigonometric functions and their component representation in a circle.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Angle(C, A, B) → α
  4. Segment(A, B) → a
  5. Segment(A, D) → b
  6. Segment(A, E) → d
  7. Segment(H, C) → e
  8. Segment(F, G) → f
  9. Segment(B, E) → g
  10. Segment(B, D) → h
  11. Ray(A, B) → i
  12. Point(i) → I
  13. Segment(A, N) → j
  14. Segment(A, M) → k
  15. Angle(C, A, N) → β
  16. Angle(C, A, M) → γ
  17. Intersect(c, k, 1) → J
  18. Segment(D, J) → n
  19. Intersect(c, j, 1) → K
  20. Segment(E, K) → p
  21. Ray(A, K) → r
  22. Point(r) → L
  23. Ray(A, M) → s
  24. Point(s) → P