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Symmetry of the Cosine Curve

Symmetry of the Cosine Curve
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2015-12-03 03:06
FunctionTrigonometryGeometric Construction
This example demonstrates the symmetry of the cosine curve. Key mathematical concepts include trigonometry and symmetry. Using GeoGebra commands such as Intersect, Semicircle, and Point, the construction of the symmetric cosine graph is illustrated. Suitable for high school mathematics education to help students understand the properties of the cosine function.

GeoGebra Commands & Parameters

  1. Intersect(c, xAxis, 1) → J
  2. Intersect(c, xAxis, 2) → D
  3. Semicircle(J, D) → e
  4. Point(e) → B
  5. OrthogonalLine(B, xAxis) → b
  6. Intersect(b, xAxis) → A_1
  7. Segment(A_1, B) → d
  8. CircleArc(O, D, B) → f
  9. Angle(D, O, B) → α
  10. Segment(O, B) → a_2
  11. Polygon(O, A_1, B) → poly1, b_1, a_1, c_1
  12. Mirror(O, xAxis) → A'_1
  13. Mirror(A_1, xAxis) → C'
  14. Mirror(B, xAxis) → B'
  15. Polygon(A'_1, C', B') → poly1', b', a', c'
  16. CircleArc(O, B', D) → p
  17. OrthogonalLine(B, a) → g
  18. OrthogonalLine(B', a) → h
  19. Intersect(a, g) → A
  20. Intersect(a, h) → A'
  21. Polygon(O, A, B) → poly2, b_2, o, f_2
  22. Polygon(O, A', B') → poly3, b'_1, o_1, h_1
  23. OrthogonalLine(C, xAxis) → i
  24. OrthogonalLine(E, xAxis) → j
  25. Segment(I, K) → k
  26. Intersect(j, xAxis) → L
  27. Intersect(i, xAxis) → M
  28. Segment(L, E) → l
  29. Segment(M, C) → m
  30. Segment(G, M) → n
  31. Segment(G, L) → q