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Formation of Trigonometric Functions

Formation of Trigonometric Functions
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2018-04-23 16:45
CircleFunctionTrigonometry
Explore the formation of sine, cosine, and tangent functions by tracing angles on the unit circle. This example covers key concepts such as the unit circle, angles, and segments, using GeoGebra commands like Point, Circle, Intersect, Rotate, Angle, and Segment. Suitable for high school math education and students learning trigonometry.

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 on a coordinate system and mark a point on the x-axis. Draw a tangent line from this point to the circle. Rotate the point on the x-axis around the circle by an angle to get a new point. Connect the original point and the new point. Draw a perpendicular line from the new point to the x-axis to find another intersection point. Connect the origin to the new point and find the intersection of the tangent line and the perpendicular line. Finally, draw all the points and line segments to illustrate the formation of sine, cosine, and tangent functions.
The prompt above was compiled from the original drawing commands and is for reference only.