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Phantom Graph of cos(x^2/2)

Phantom Graph of cos(x^2/2)
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2018-07-31 07:14
FunctionTrigonometryGraphing
In collections Phantom Graphs
This example demonstrates the phantom graph of the function cos(x^2/2). It involves the concept of trigonometric functions. Using GeoGebra commands such as Plane, CurveCartesian, Sequence, etc., the graph of the function can be constructed. Suitable for high school mathematics education or learning.

GeoGebra Commands & Parameters

  1. Plane((0, c, 0), (1, c, 0), (0, c, 1)) → p
  2. CurveCartesian(0, cos(t^(2) / 2), t, t, -25, 25) → a
  3. Sequence(CurveCartesian[sqrt(t^(2) + ((2 * k) * π)), ((-1)^(k) * cosh((t * sqrt(t^(2) + ((2 * k) * π))))), t, t, -25, 25], k, -10, 10) → Curve1
  4. Sequence(CurveCartesian[(-sqrt(t^(2) + ((2 * k) * π))), ((-1)^(k) * cosh((t * sqrt(t^(2) + ((2 * k) * π))))), t, t, -25, 25], k, -10, 10) → Curve2
  5. Sequence(((-sqrt((2 * acos(c)) + ((4 * k) * π))), c), k, -5, 5) → PtsCR2
  6. Sequence((sqrt((2 * acos(c)) + ((4 * k) * π)), c), k, -5, 5) → PtsCR1
  7. Sequence((sqrt(((4 + (4 * k)) * π) - (2 * acos(c))), c, 0), k, -5, 5) → PtsCR3
  8. Sequence(((-sqrt(((4 + (4 * k)) * π) - (2 * acos(c)))), c, 0), k, -5, 5) → PtsCR4
  9. Sequence((0, c, sqrt(((4 + (4 * k)) * π) - (2 * acos(c)))), k, 0, 5) → PtsCosPHG3
  10. Sequence((0, c, sqrt((2 * acos(c)) + ((4 * k) * π))), k, 0, 5) → PtsCosPHG1
  11. Sequence((0, c, (-sqrt((2 * acos(c)) + ((4 * k) * π)))), k, 0, 5) → PtsCosPHG2
  12. Sequence((0, c, (-sqrt(((4 + (4 * k)) * π) - (2 * acos(c))))), k, 0, 5) → PtsCosPHG4
  13. Sequence((sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh(c)^(2))), c, sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh(c)^(2)))), k, -6, 6, 2) → PtsCoshPG1
  14. Sequence(((-sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh(c)^(2)))), c, sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh(c)^(2)))), k, -6, 6, 2) → PtsCoshPG2
  15. Sequence((sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh(c)^(2))), c, (-sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh(c)^(2))))), k, -6, 6, 2) → PtsCoshPG3
  16. Sequence(((-sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh(c)^(2)))), c, (-sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh(c)^(2))))), k, -6, 6, 2) → PtsCoshPG4
  17. Sequence((sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2))), c, sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2)))), k, -5, 7, 2) → PtsCoshPG5
  18. Sequence(((-sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2)))), c, sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2)))), k, -5, 7, 2) → PtsCoshPG6
  19. Sequence((sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2))), c, (-sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2))))), k, -5, 7, 2) → PtsCoshPG7
  20. Sequence(((-sqrt((π * k) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2)))), c, (-sqrt((-((π * k))) + sqrt((k^(2) * π^(2)) + acosh((-c))^(2))))), k, -5, 7, 2) → PtsCoshPG8

AI Drawing Prompt Reference

Draw the phantom graph of the function cos(x^2/2). Start by drawing a plane on the x-axis, then plot the main curve. Use sequence commands to draw a series of phantom lines around the main curve, extending upwards and downwards with varying k values. Finally, plot a series of points around the main curve to form the endpoints of the phantom lines.
The prompt above was compiled from the original drawing commands and is for reference only.