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Translations of Trig Functions

Translations of Trig Functions
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2015-01-27 05:49
FunctionTrigonometryGraphing
This example demonstrates the translation transformations of sine and cosine function graphs. It involves core math concepts like function graph translation, amplitude, phase shift, and period. Constructed using GeoGebra commands and objects like RandomElement, Random, Textfield, If, verticalshift, amplitude, phaseshift, and sliders. Suitable for high school students learning trigonometric function graph transformations.

GeoGebra Commands & Parameters

  1. RandomElement({-3.142, -1.571, -0.786, 0, 0.786, 1.571, 3.142}) → c
  2. Random(-3, 3) → d
  3. Random(-3, 3) → a
  4. RandomElement({0.5, 1, 2, 4, 8}) → b
  5. Textfield(input) → inputBox1
  6. Textfield(per_1) → inputBox2
  7. Textfield(per_2) → inputBox3
  8. If(h_1 ≟ a_1 ∧ per_1 ≟ 1.57, 1, 0) → score_1
  9. If(per_2 ≟ 12.56 ∧ h_2 ≟ a_2, 1, 0) → score_2
  10. Textfield(per_3) → inputBox4
  11. If(h_3 ≟ a_3 ∧ per_3 ≟ 6.28, 1, 0) → score_3
  12. Textfield(per_4) → inputBox5
  13. If(per_4 ≟ 3.14 ∧ a_4 ≟ h_4, 1, 0) → score_4
  14. Textfield(per_5) → inputBox6
  15. If(a_5 ≟ h_5 ∧ per_5 ≟ 3.14, 1, 0) → score_5

AI Drawing Prompt Reference

Draw the translation transformations of sine and cosine function graphs, showing different amplitudes, phase shifts, and periods, with randomly generated amplitudes, phase shifts, and vertical translations, and include text boxes for input and judgment of whether the period and amplitude match, finally generating a graph containing sine and cosine images and their transformations.
The prompt above was compiled from the original drawing commands and is for reference only.