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Definition of Trigonometric Functions

Definition of Trigonometric Functions
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2017-02-05 02:28
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the definition of trigonometric functions, showing the relationship between points on the unit circle and trigonometric values. Using GeoGebra commands such as Sequence, Element, and Point, the example dynamically displays the graphs of sine, cosine, and tangent functions. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(t, t, -3, 3, 1 / n) → seq
  2. Element(afun, Example) → f
  3. Point(yAxis) → A
  4. Vector(A, f_A) → u
  5. Textfield(f) → inputBox1
  6. Vector(A, g_A) → v
  7. Element(fun_1, Example) → f_1
  8. Zip((4, f_1(f(k))), k, seq) → list8
  9. Zip((2, f(k)), k, seq) → list3
  10. Zip(Vector[A, j], A, list3, j, list8) → list9
  11. Sequence((2, k), k, -1.5708, 3.241592653589793, 0.2618) → list5
  12. Vector(f_A, A') → w
  13. Zip(Vector[(0, k), (2, f(k))], k, seq) → list1
  14. Zip((0, k), k, seq) → list2
  15. Zip((k, f(k)), k, seq) → list4

AI Drawing Prompt Reference

Draw the relationship between points on the unit circle and the sine, cosine, and tangent functions. Start by drawing the unit circle, then dynamically generate a series of points on the circle to illustrate the graphs of the sine and cosine functions, using vectors to represent the lines from the origin to these points. Next, draw the graph of the tangent function and use vectors to represent the tangent values.
The prompt above was compiled from the original drawing commands and is for reference only.