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Trigonometric Functions and Circle Intersections

Trigonometric Functions and Circle Intersections
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2017-01-27 04:00
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the intersections between trigonometric function graphs and a unit circle, highlighting geometric properties and coordinate relationships. Core concepts include trigonometric functions, unit circle, intersection points, angle-radius conversion. GeoGebra commands like Point, Intersect, Circle, Segment, Angle, OrthogonalLine, CircleArc, and Vector are used in construction. Suitable for high school mathematics education to understand the geometric connection between trigonometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Element(fnl, function) → g
  2. Point(yAxis) → E
  3. Intersect(xAxis, yAxis) → A
  4. Circle(A, B) → c
  5. Segment(A, C) → a
  6. Segment(B, A) → b
  7. Angle(B, A, C) → α
  8. OrthogonalLine(C, yAxis) → d
  9. Intersect(d, yAxis) → D
  10. CircleArc(A, B, C) → e
  11. Vector(C, D) → u
  12. Vector(E, F) → v
  13. Segment(D, A) → h
  14. Segment(H, B) → i
  15. Vector(t, C) → w
  16. OrthogonalLine(C, b) → j
  17. Intersect(j, i) → I
  18. Vector(C, I) → z
  19. Vector(I, J) → k
  20. Vector(E, K) → l
  21. Vector(L, K) → n
  22. Segment(t, M) → q
  23. Segment(E, L) → r
  24. Segment(S, U) → b_1
  25. Segment(P, Q) → c_1
  26. Segment(R, T) → a_1
  27. Vector(M, V) → p
  28. Vector(C_1, W) → v_1
  29. Segment(V, A) → g_1
  30. Vector(L, A_1) → m
  31. Element(fnnl, function) → fnn
  32. Vector(V, I) → w_1
  33. Vector(C_1, W) → u_1
  34. Vector(I, C_1) → z_2
  35. Vector(V, Z) → z_1
  36. Vector(C, W) → h_1
  37. Vector(C, W) → i_1
  38. Vector(V, Z) → j_1
  39. Segment(A, V) → k_1