MathPlotAI Logo MathPlotAI

Trigonometry & the Unit Circle

Trigonometry & the Unit Circle
Loading the math board and drawing, please wait…
2017-01-14 07:20
CircleTrigonometryGeometric ConstructionGraphing
This example dynamically demonstrates the relationship between trigonometric function values and angles by showing the movement of a point on the unit circle. It involves core concepts like the definition of trigonometric functions, the unit circle, angle measurement, and coordinate geometry. GeoGebra commands such as Segment, Point, Intersect, Circle, Rotate, and Angle are used in the construction. Suitable for high school mathematics teaching to help students visually understand the origin and properties of trigonometric function graphs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(xAxis) → C
  3. Segment(C, D) → b
  4. Segment(E, F) → c
  5. Segment(G, H) → d
  6. Point(yAxis) → I
  7. Segment(I, J) → e
  8. Segment(K, L) → f
  9. Point(xAxis) → M
  10. Segment(M, N) → g
  11. Point(yAxis) → O
  12. Segment(O, P) → h
  13. Intersect(a, b) → Q
  14. Circle(Q, 1) → k
  15. Point(g) → R
  16. Circle(R, 1) → p
  17. Point(c) → S
  18. Circle(S, 1) → q
  19. Intersect(e, f) → T
  20. Circle(T, 1) → r
  21. Intersect(q, d, 1) → W
  22. Intersect(r, e, 2) → Z
  23. Intersect(k, a, 2) → U
  24. Intersect(p, h, 2) → V
  25. Rotate(V, θ, R) → V'
  26. Angle(V, R, V') → α
  27. Rotate(U, (-θ), Q) → U'
  28. Angle(U', Q, U) → β
  29. Rotate(W, θ, S) → W'
  30. Angle(W, S, W') → γ
  31. Point(k) → A_1
  32. Intersect(q, d, 2) → B_1
  33. Segment(R, V') → i
  34. Segment(Q, U') → j
  35. Segment(S, W') → l
  36. Rotate(Z, (-θ), T) → Z'
  37. Angle(Z', T, Z) → δ
  38. Segment(T, Z') → m
  39. Angle(A_1, Q, U') → ε
  40. Angle(B_1, S, W') → ζ
  41. Angle(Z, T, Z') → η
  42. Segment(U', C_1) → n
  43. Segment(C_1, Q) → s
  44. Segment(R, D_1) → t
  45. Segment(D_1, V') → a_1
  46. Segment(W', F_1) → b_1
  47. Segment(F_1, S) → c_1
  48. Segment(T, H_1) → d_1
  49. Segment(H_1, Z') → e_1