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Unit Circle and Trigonometric Functions by ayoob

Unit Circle and Trigonometric Functions by ayoob
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2012-06-08 22:03
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Trigonometric Graphs and the Unit Circle wellington point
This example demonstrates the relationship between the unit circle and sine and tangent functions through dynamic visualization of red and green line coordinates corresponding to trigonometric values. Core math concepts include the unit circle, sine, tangent, and coordinate geometry. It is constructed using GeoGebra commands like Point, Circle, Intersect, Rotate, Angle, Segment, OrthogonalLine, Tangent, Line, Ray, suitable for high school mathematics teaching to understand the definition and graph of trigonometric functions.

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 trigonometric function graph. The circle has center at the origin and radius 1. Draw a horizontal and vertical axis. Take a point B on the circle, rotate it to get point P. Draw a segment from A to P, and draw a line perpendicular to the horizontal axis intersecting the horizontal axis at point C. Draw the tangent to the circle at B and the line from A to P, their intersection is D. Connect A to C and C to P. Draw a segment from B to D and a ray from D to C. Connect other points to form the graph. Ensure the graph is clear, showing the unit circle, trigonometric values, and coordinate relationships.
The prompt above was compiled from the original drawing commands and is for reference only.