MathPlotAI Logo MathPlotAI

Trigonometric & Linear Transformations Demo

Trigonometric & Linear Transformations Demo
Loading the math board and drawing, please wait…
2017-02-25 10:17
FunctionTrigonometryCalculus
This example demonstrates the linear transformations of trigonometric functions and their loci in a coordinate plane. It involves core concepts like trigonometry, linear functions, derivatives, and transformations. Constructed using GeoGebra commands like Point, Vector, Segment, Sequence, Textfield, Derivative, Zip, it is ideal for high school and above students to explore function transformations and calculus applications.

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

AI Drawing Prompt Reference

Draw a trigonometric function and its linear transformation locus in a coordinate plane, showing the original function, vertical translation vector, symmetric line segments, and transformed function images, with the origin, symmetry axis, and transformation vectors labeled, and finally plot multiple linearly transformed function images with an input box for interaction.
The prompt above was compiled from the original drawing commands and is for reference only.