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Sine and Cosine Curves from Unit Circle by mathspace

Sine and Cosine Curves from Unit Circle by mathspace
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2015-11-18 18:17
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to derive sine and cosine curves using the unit circle. It involves core math concepts like the unit circle, trigonometric functions, angles, and coordinate geometry. Construction highlights include using GeoGebra commands and objects such as Point, Circle, Intersect, Rotate, Angle, Segment, OrthogonalLine, and Ray. Suitable for high school mathematics education to visually explain the generation process of trigonometric function graphs.

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