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Graphing Sine and Cosine Functions (All Transformations)

Graphing Sine and Cosine Functions (All Transformations)
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2021-10-07 18:44
FunctionTrigonometryCoordinate GeometryGraphing
This example demonstrates the graphing of sine and cosine functions along with all possible transformations. Key math concepts include trigonometric functions, function graph transformations, and coordinate systems. It is constructed using GeoGebra commands like Textfield, Point, FitSin, Sequence, Union, RandomElement, Random, If, and involves objects such as sliders and input boxes for dynamic parameter adjustments. Ideal for high school mathematics teaching and function transformation studies.

GeoGebra Commands & Parameters

  1. Textfield(start) → InputBox1
  2. Textfield(end) → InputBox2
  3. Textfield(k1) → InputBox3
  4. Textfield(k2) → InputBox4
  5. Textfield(k3) → InputBox5
  6. Point(eq6) → A
  7. Point(eq7) → B
  8. Point(eq8) → C
  9. Point(eq9) → D
  10. Textfield(a) → InputBox6
  11. Textfield(b) → InputBox7
  12. Point(eq10) → E
  13. Point(eq7) → F
  14. FitSin({A, C, D, E, F}) → f
  15. Sequence(i, i, -6, -0.5, 0.5) → ampLeftList, {-6, -5.5, -5, -4.5, -4, -3.5, -3, -2.5, -2, -1.5, -1, -0.5}
  16. Sequence(i, i, 0.5, 6, 0.5) → ampRightList, {0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6}
  17. Union(ampLeftList, ampRightList) → ampList
  18. RandomElement(ampList) → amp
  19. RandomElement(Sequence[i, i, -8, 8, 0.5]) → dval
  20. RandomElement({1, 2, 3, 4, 5}) → bnum
  21. RandomElement({1, 2, 3, 4, 5}) → bdenom
  22. RandomElement({1, 2, 3, 4, 5}) → cnum
  23. RandomElement({1, 2, 3, 4, 5}) → cdenom
  24. Random(1, 2) → cc
  25. If(cc ≟ 1, (amp * sin(((bnum / bdenom * π) * x) - (cnum / cdenom * π))) + dval, (amp * cos(((bnum * π / bdenom) * x) - (cnum * π / cdenom))) + dval) → p

AI Drawing Prompt Reference

Draw a graph of sine and cosine functions with dynamic parameter adjustments. Include input boxes and points for adjusting amplitude, frequency, and phase. The graph shows transformed sine and cosine curves connected by points. This graph is useful for teaching function transformation concepts.
The prompt above was compiled from the original drawing commands and is for reference only.