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Sine and Cosine Curves from Unit Circle

Sine and Cosine Curves from Unit Circle
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2019-10-22 01:33
CircleTrigonometryGeometric Construction
This example demonstrates sine and cosine curves using the unit circle. It involves key mathematical concepts such as trigonometry. Using GeoGebra commands like Point, Circle, Intersect, Rotate, etc., dynamic sine and cosine curves can be constructed. Suitable for high school mathematics education, particularly in coordinate geometry and 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. Segment(C, P) → g
  10. Ray(H, U) → q
  11. Ray(I, V) → r
  12. Segment(V, U) → l
  13. Segment(X, W) → m
  14. Segment(Z, Y) → n
  15. Segment(G, F) → p
  16. Segment(J, K) → s
  17. Segment(K, O) → t
  18. Segment(K, Q) → a_1
  19. Segment(M, A_1) → b_1
  20. Segment(M, B_1) → c_1
  21. Segment(J, C_1) → d_1
  22. Segment(J, D_1) → e_1
  23. Segment(L, N) → f_1
  24. Segment(L, E) → g_1
  25. Segment(M, M') → h_1
  26. Segment(C, P) → e
  27. Segment(A, C) → f
  28. Point(yAxis) → R
  29. Point(yAxis) → T
  30. Segment(R, T) → h

AI Drawing Prompt Reference

Draw a unit circle and construct sine and cosine curves based on it. Start by creating point A on the x-axis, then draw a circle c with A as the center and radius 1. Circle c intersects the x-axis at two points, take the right intersection point B, rotate B around A to get point P, measure the angle ∠BAP to get angle β, draw line segment AP, then draw the perpendicular line b to AP, which intersects the x-axis at point C, and draw line segment CP. Next, draw two perpendicular lines q and r to the x-axis, and line segments l, m, n, p, s, t, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, and finally draw line segments h, e, and f.
The prompt above was compiled from the original drawing commands and is for reference only.