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Unit Circle and Inverse Trig Graphs

Unit Circle and Inverse Trig Graphs
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2019-08-13 04:36
CircleFunctionTrigonometryCoordinate GeometryCalculus
This example demonstrates the relationship between the unit circle and graphs of sine, cosine, tangent, and inverse trigonometric functions. It involves core math concepts like the unit circle definition, trigonometric functions, inverse trigonometric functions, derivatives, and analytical geometry. Construction uses GeoGebra commands such as Line, Point, Segment, Intersect, Circle, Angle, and OrthogonalLine. Suitable for high school and above mathematics learning to understand trigonometric properties and graph transformations.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. Point(a) → B_1
  3. Segment(A, B_1) → b
  4. Intersect(xAxis, yAxis) → D
  5. Circle(A, b) → c
  6. Point(c) → C
  7. Segment(A, C) → d
  8. Angle(B_1, A, C) → α
  9. Point(Circle[D, α]) → E
  10. Segment(D, E) → e
  11. OrthogonalLine(C, b) → h_1
  12. Intersect(h_1, a) → F
  13. Segment(C, F) → Sine
  14. Intersect(c, a, 2) → G
  15. Segment(G, A) → i
  16. Segment(A, F) → Cosine
  17. OrthogonalLine(C, d) → j
  18. Intersect(a, j) → H
  19. Segment(C, H) → Tangent
  20. Segment(B_1, H) → k_1
  21. OrthogonalLine(E, xAxis) → l
  22. Intersect(g, l, (0.6775728175269462, 0.782731011348612)) → I
  23. Intersect(f, l, (0.6775728175269462, 0.6298282915862481)) → J
  24. Intersect(n, l, (0.6775728175269462, 0.8084084484644634)) → K
  25. Segment(J, E) → q
  26. Segment(I, E) → r
  27. Segment(K, E) → p
  28. Intersect(f_1, l, (0.6775728175269462, 1.6025820473500487)) → L
  29. Intersect(g_1, l, (0.6775728175269462, 1.289525390427809)) → M
  30. Intersect(n_1, l, (0.6775728175269462, 1.2485662599475453)) → N
  31. OrthogonalLine(C, d) → a_1
  32. OrthogonalLine(A, i) → b_1
  33. Intersect(a_1, b_1) → O
  34. Segment(O, C) → Cotangent
  35. OrthogonalLine(N, xAxis) → c_1
  36. Intersect(c_1, xAxis) → P
  37. Segment(N, P) → d_1
  38. Line(A, B_1) → s
  39. OrthogonalLine(C, d) → e_1
  40. Intersect(s, e_1) → Q
  41. Segment(C, Q) → i_1
  42. Segment(A, Q) → Secant
  43. OrthogonalLine(M, xAxis) → j_1
  44. Intersect(j_1, xAxis) → R
  45. Segment(M, R) → l_1
  46. OrthogonalLine(A, i) → m_1
  47. OrthogonalLine(C, d) → p_1
  48. Intersect(m_1, p_1) → S
  49. Segment(S, A) → Cosecant
  50. OrthogonalLine(L, xAxis) → q_1
  51. Intersect(q_1, xAxis) → T
  52. Segment(L, T) → r_1
  53. Intersect(c, b, 1) → U

AI Drawing Prompt Reference

Draw the unit circle and its relationship with sine, cosine, tangent, and inverse trigonometric functions. Start by drawing the x-axis and the unit circle, then use points on the unit circle to draw sine, cosine, and tangent segments. Next, sketch the graphs of inverse trigonometric functions, and finally connect key points to form the unit circle and inverse trigonometric function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.