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Trigonometric Function Transformation Example

Trigonometric Function Transformation Example
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2017-02-25 03:43
FunctionTrigonometryTransformation
This example demonstrates the transformation of trigonometric functions, showing the basic properties and transformation rules of trigonometric functions. Using GeoGebra commands, dynamic observation of the changes in trigonometric function graphs can be achieved. The construction summary mentions the use of Element, Point, Vector, Segment, Sequence, Textfield, Derivative, Zip, etc. It is suitable for high school mathematics teaching and learning of trigonometric function transformations.

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