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Chebyshev Polynomial of the First Kind

Chebyshev Polynomial of the First Kind
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2022-01-12 17:51
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the graph and properties of the Chebyshev Polynomial of the First Kind. It involves core mathematical concepts such as polynomial functions, trigonometric functions, and geometric transformations. The construction uses GeoGebra commands like Simplify, Expand, and TableText, along with objects A1 to A15, l1, and text1. It is suitable for high school and above students to understand the image characteristics and transformation rules of polynomial functions.

GeoGebra Commands & Parameters

  1. Simplify(((2 * x) * A2(x)) - A1) → A3
  2. Simplify(((2 * x) * A3(x)) - A2(x)) → A4
  3. Simplify(((2 * x) * A4(x)) - A3(x)) → A5
  4. Simplify(((2 * x) * A5(x)) - A4(x)) → A6
  5. Simplify(((2 * x) * A6(x)) - A5(x)) → A7
  6. Simplify(((2 * x) * A7(x)) - A6(x)) → A8
  7. Simplify(((2 * x) * A8(x)) - A7(x)) → A9
  8. Simplify(((2 * x) * A9(x)) - A8(x)) → A10
  9. Simplify(((2 * x) * A10(x)) - A9(x)) → A11
  10. Simplify(((2 * x) * A11(x)) - A10(x)) → A12
  11. Expand(Simplify[((2 * x) * A12(x)) - A11(x)]) → A13
  12. Simplify(((2 * x) * A13(x)) - A12(x)) → A14
  13. Simplify(((2 * x) * A14(x)) - A13(x)) → A15
  14. TableText(l1, "v") → text1

AI Drawing Prompt Reference

Draw a graph demonstrating the properties of the first kind Chebyshev polynomial, involving polynomial and trigonometric functions, showing geometric transformations step by step to illustrate its characteristics, starting from basic functions and building up to present the polynomial graph and its transformation rules, suitable for high school and above students.
The prompt above was compiled from the original drawing commands and is for reference only.