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Unit Circle and Trigonometric Functions (Animated)

Unit Circle and Trigonometric Functions (Animated)
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2019-08-13 04:42
CircleFunctionTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the unit circle with the y-coordinates of the red and green lines representing the sine and tangent functions, respectively. Using commands like rotation, intersection, and angle, it dynamically illustrates the geometric meaning of trigonometric functions. Suitable for high school and above students to learn about trigonometric functions and the unit circle.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, α, A) → P
  5. Angle(B, A, P) → β
  6. Segment(A, P) → a
  7. OrthogonalLine(P, xAxis) → b
  8. Intersect(b, xAxis) → C
  9. Tangent(B, c) → d,
  10. Line(A, P) → e
  11. Intersect(e, d) → D
  12. Segment(A, C) → f
  13. Segment(C, P) → g
  14. Segment(B, D) → h
  15. Ray(H, U) → q
  16. Ray(I, V) → r
  17. Segment(V, U) → l
  18. Segment(X, W) → m
  19. Segment(Z, Y) → n
  20. Segment(G, F) → p
  21. Segment(J, K) → s
  22. Segment(K, O) → t
  23. Segment(K, Q) → a_1
  24. Segment(M, A_1) → b_1
  25. Segment(M, B_1) → c_1
  26. Segment(J, C_1) → d_1
  27. Segment(J, D_1) → e_1
  28. Segment(L, N) → f_1
  29. Segment(L, E) → g_1
  30. Segment(M, M') → h_1
  31. Segment(P, S) → j
  32. Segment(D, T) → i_1

AI Drawing Prompt Reference

Draw a unit circle and select a point P on the circle, then rotate it around the origin to get point P. Draw a tangent line at point P and let it intersect the x-axis at point D. Connect points A, P, B, and D to form a triangle. Use a slider to adjust the angle and dynamically illustrate the geometric meaning of sine and tangent functions.
The prompt above was compiled from the original drawing commands and is for reference only.