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Trigonometric Composite Transformations and Geometric Mean Demo

Trigonometric Composite Transformations and Geometric Mean Demo
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2017-02-25 03:06
FunctionTrigonometrySequenceDerivativeGraphing
①This GeoGebra example dynamically demonstrates composite transformations of trigonometric functions (e.g., shifts and stretches) and their visual connection to geometric mean, median, and other statistical concepts, supported by histograms and conic sections. ②Core mathematical concepts include trigonometric function transformations, geometric mean, median, conic sections, sequences, and basic derivatives. ③Construction highlights: using commands such as Element, Point, Vector, Segment, Sequence, Textfield, Derivative, and Zip to create objects B, C, TrigFn, k, A, TrigL, f, a_1, a, f_a, u, along with multiple auxiliary points (A1–A14, B1–B7) and function graphs, enabling interactive parameter adjustment via sliders and text inputs. ④Suitable for high school to early college students, ideal for math lab activities or self-exploration, helping to understand geometric meanings of function transformations and statistical measures, and serving as a reference for teachers creating dynamic lessons.

GeoGebra Commands & Parameters

  1. Element(TrigL, TrigFn) → f
  2. Point(yAxis) → a
  3. Vector(a, f_a) → u
  4. Segment(C_1, D) → e
  5. Vector(E, F) → v
  6. Sequence((k, f(k)), k, C - π, C + π, 0.5235987755982988) → list1
  7. Sequence(Vector[(0, k), (2, f(k))], k, C - π, C + π, 0.5235987755982988) → list2
  8. Sequence(Segment[(i, f(i)), ((2 * C) - i, f((2 * C) - i))], i, C - π, C, 0.5235987755982988) → list3
  9. Vector(G, H) → w
  10. Segment(f_x, J) → j
  11. Sequence(Segment[(i, f(i)), (π - i, f(π - i))], i, 0, 3.141592653589793, 0.5235987755982988) → supl
  12. Textfield(B) → inputBox1
  13. Textfield(C) → InputBox1
  14. Derivative(f) → f'
  15. Vector(f_a, (2, y(f_a) + f'(y(a)))) → h
  16. Sequence(-5, 5) → nlist
  17. Zip(((1 / B * ((2 * k) + 1)) * π / 2) - C / B, k, nlist) → xtrslist
  18. Zip((z, f(z)), z, xtrslist) → xtrspts
  19. Zip(((1 / B * k) * π) - C / B, k, nlist) → xrtclist
  20. Zip((z, f(z)), z, xrtclist) → xtrcpts
  21. Textfield(A) → InputBox2
  22. Segment(a, Q) → l
  23. Segment(a, P) → m
  24. Vector(P, f_a) → n
  25. Vector(Q, f_a) → p
  26. Segment(f_x, M) → s
  27. Segment(f_x, R) → q