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Transforming the Sine Function (All Transformations)

Transforming the Sine Function (All Transformations)
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2019-01-18 00:52
FunctionTrigonometryTransformationGraphing
This example demonstrates the sine function graph and all its transformations. It involves core math concepts like sine function, geometric transformations, and coordinate systems. Construction highlights include commands like Textfield, FractionText, Numerator, Denominator, Dilate, LCM, Vector, Translate, Distance, Intersect, and objects a, c, d, f, etc. Suitable for high school and above students to understand function transformation rules.

GeoGebra Commands & Parameters

  1. Textfield(c) → InputBox1
  2. FractionText(1.25) → text1
  3. Numerator(b_1) → e
  4. Denominator(b_1) → g
  5. Dilate(A, If[0 < h ≤ 1, 1 - h, 0], B) → A'
  6. LCM(4, g) → i
  7. Dilate(A, If[2 < h ≤ 3, 3 - h, 0], C) → A'_1
  8. Vector(A, A'_1) → u
  9. Translate(q, u) → q_1
  10. Dilate(E, If[1 < h ≤ 2, 2 - h, 0], D) → E'
  11. Vector(E, E') → v
  12. Translate(E, u) → E'_1
  13. Translate(D, u) → D'
  14. Vector(E'_1, D') → w
  15. Dilate(G, If[6 < h ≤ 7, 7 - h, 0], I) → G'
  16. Vector(G, G') → m
  17. Translate(F, m) → F'
  18. Translate(G, m) → G'_1
  19. Translate(C, m) → C'
  20. Distance(C, C') → distanceCC'
  21. Distance(F', I) → distanceF'I
  22. Distance(A, C) → distanceAC
  23. Distance(J, K) → a_1
  24. Intersect(k_1, l_1) → S
  25. Intersect(l_1, j_1) → T
  26. Dilate(S, If[3 < h ≤ 4, 4 - h, 0], T) → S'
  27. Vector(S, S') → v_1
  28. Distance(S, T) → distanceST
  29. Dilate(S, If[4 < h ≤ 5, 5 - h, 0], T) → S'_1
  30. Dilate(D', If[4 < h ≤ 5, 5 - h, 0], U) → D''
  31. Vector(D', D'') → w_1
  32. Translate(P, w_1) → P'
  33. Translate(D', w_1) → D''_1
  34. Vector(P', D''_1) → c_1
  35. Distance(P', D''_1) → distanceP'D''1
  36. Dilate(U, If[5.5 < h ≤ 6.5, 6.5 - h, 0], V) → U'
  37. Vector(M, U') → l
  38. Distance(M, U') → distanceMU'
  39. Dilate(A_1, If[7 < h ≤ 8, 8 - h, 0], Z) → B_1
  40. Vector(A_1, B_1) → n
  41. Translate(t_1, n) → r
  42. Translate(M, n) → M'
  43. Translate(U', n) → U''
  44. Vector(M', U'') → s
  45. Distance(U'', M') → distanceU''M'
  46. Distance(A_1, B_1) → distanceA1B1
  47. Textfield(d) → InputBox2
  48. Textfield(a) → InputBox3
  49. Textfield(b) → InputBox4

AI Drawing Prompt Reference

Draw the sine function and all its transformations, including vertical and horizontal scaling, translation, and reflection. Start by drawing the sine function graph, then apply various transformations such as translating point A along vector u to get q₁, translating point E along vector v to get E₁, and translating point D along vector w to get D'. Calculate the distances between various points. Finally, use reflection and scaling transformations to get the final graph, demonstrating the rules of sine function transformations.
The prompt above was compiled from the original drawing commands and is for reference only.