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Unit Circle Trig Ratios

Unit Circle Trig Ratios
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2015-02-13 22:51
CircleTrigonometryGeometric Construction
This example demonstrates the trigonometric ratios on the unit circle. By constructing points on the unit circle, it shows the changes in sine, cosine, and tangent values. Commands used include Circle, Point, Intersect, If, Ray, Line, etc. Suitable for high school math education to help students understand basic trigonometric concepts.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Point(c) → P
  3. Intersect(xAxis, yAxis) → O
  4. If(y(P) ≥ y(A), Distance[P, A], (-Distance[P, A])) → sinVal
  5. Ray(O, P) → a
  6. Line((0, 1), (1, 1)) → b
  7. Line((1, 0), (1, 1)) → d
  8. Intersect(b, d) → C
  9. Intersect(d, a) → Q
  10. Intersect(b, a) → X
  11. Intersect(c, b) → D,
  12. Intersect(d, xAxis) → B
  13. Angle(B, O, P) → θ
  14. If(x(A) ≥ x(O), Distance[O, A], (-Distance[O, A])) → cosVal
  15. Segment(P, A) → e
  16. Line((-1, 0), (-1, -1)) → d'
  17. Intersect(d', a) → Q'
  18. Intersect(c, d', 1) → B'
  19. If(x(P) ≥ 0, If[(sinVal * cosVal) ≥ 0, Distance[B, Q], (-Distance[B, Q])], If[(sinVal * cosVal) ≥ 0, Distance[B', Q'], (-Distance[B', Q'])]) → tanVal
  20. Intersect(b', a) → X'
  21. If(x(P) ≥ 0, If[cosVal ≥ 0, Distance[O, Q], (-Distance[O, Q])], If[cosVal ≥ 0, Distance[O, Q'], (-Distance[O, Q'])]) → secVal
  22. If(y(P) ≥ 0, If[(sinVal * cosVal) ≥ 0, Distance[D, X], (-Distance[D, X])], If[(sinVal * cosVal) ≥ 0, Distance[D', X'], (-Distance[D', X'])]) → cotVal
  23. If(y(P) ≥ 0, If[sinVal ≥ 0, Distance[O, X], (-Distance[O, X])], If[sinVal ≥ 0, Distance[O, X'], (-Distance[O, X'])]) → cosecVal
  24. Locus(Y_{cosec}, P) → cosecLocus
  25. Segment(P_0, Y_{cosec}) → g
  26. Locus(Y_{sec}, P) → cotLocus
  27. Segment(P_0, Y_{sec}) → h
  28. Locus(Y_{cot}, P) → loc3
  29. Segment(Y_{cot}, P_0) → j
  30. Locus(Y_{sin}, P) → sinLocus
  31. Segment(Y_{sin}, P_0) → l
  32. Locus(Y_{cos}, P) → cosLocus
  33. Segment(Y_{cos}, P_0) → n
  34. Locus(Y_{tan}, P) → tanLocus
  35. Segment(Y_{tan}, P_0) → p
  36. Segment(P, A) → f_1
  37. Segment(O, A) → g_1
  38. Segment(Q, B) → j_1
  39. Segment(B', Q') → k_1
  40. Segment(O, X) → l_1
  41. Segment(O, X') → m_1
  42. Segment(O, Q) → n_1
  43. Segment(Q', O) → p_1
  44. Segment(D, X) → q_1
  45. Segment(X', D') → r_1
  46. Segment(O, A) → s_1
  47. Angle(P, A, O) → α

AI Drawing Prompt Reference

Draw a unit circle and mark a point on it, showing its intersections with the coordinate axes. Draw a ray from the origin to the point and intersect it with reference lines to get several key points. Calculate and display the sine, cosine, and tangent values using these points, with different colors or line styles. Finally, plot the loci of sine, cosine, tangent, cotangent, secant, and cosecant to show their relationships with the angle.
The prompt above was compiled from the original drawing commands and is for reference only.