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Sine vs Cosine Exploration

Sine vs Cosine Exploration
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2018-12-02 00:46
AngleFunctionTrigonometryGeometric Construction
This example demonstrates the geometric meaning of sine and cosine in a right triangle. It involves core math concepts like trigonometric function definitions and side-angle relationships in right triangles. Construction highlights include using GeoGebra commands such as Intersect, Segment, Point, OrthogonalLine, Polygon, and Angle. Suitable for high school students learning trigonometric functions to visually understand the intrinsic connection between sine and cosine.

GeoGebra Commands & Parameters

  1. Intersect(b, d) → A
  2. Intersect(xAxis, yAxis) → B
  3. Segment(B, A) → e
  4. Intersect(d, xAxis) → C
  5. Segment(C, A) → f
  6. Segment(B, C) → g
  7. Segment(D, E) → h
  8. Segment(F, G) → i
  9. Segment(H, I) → j
  10. Segment(B, I) → k
  11. Segment(J, K) → l
  12. Segment(L, M) → m
  13. Point(yAxis) → N
  14. Point(yAxis) → O
  15. OrthogonalLine(O, yAxis) → n
  16. OrthogonalLine(N, yAxis) → p
  17. Point(n) → P
  18. OrthogonalLine(P, n) → q
  19. Intersect(p, q) → Q
  20. Polygon(O, P, Q, N) → poly1, o, p_1, q_1, n_1
  21. Segment(C, H) → r
  22. Angle(A, B, C) → α
  23. Angle(A, C, B) → β
  24. Angle(I, H, B) → γ
  25. Segment(H, B) → a_1