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Unit Circle for Angles Greater than 90

Unit Circle for Angles Greater than 90
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2015-02-08 13:33
CircleAngleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric representation of the unit circle for angles greater than 90 degrees and the behavior of trigonometric functions (sine, cosine, tangent) in the second and third quadrants. Core mathematical concepts include the unit circle, angles, trigonometric functions, and right-angled triangles. The construction utilizes GeoGebra commands/objects such as Intersect, Point, Circle, Segment, OrthogonalLine, Line, Angle, and Vector. It is suitable for high school students learning about trigonometric functions in different quadrants.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → hyp
  6. OrthogonalLine(C, xAxis) → b
  7. Line(A, xAxis) → d
  8. Angle(B, A, C) → Θ
  9. Intersect(b, d) → D
  10. Angle(C, D, A) → α
  11. Vector(A, D) → adj
  12. Vector(D, C) → opp
  13. Line(C, d) → a
  14. Intersect(c, a) → E, F
  15. Segment(A, F) → e
  16. OrthogonalLine(F, d) → f
  17. Intersect(f, d) → G
  18. Vector(G, F) → u
  19. Vector(A, G) → v
  20. Angle(A, G, F) → β
  21. Angle(F, A, G) → γ
  22. Intersect(c, f) → H, I
  23. Line(I, d) → h
  24. OrthogonalLine(I, d) → i
  25. Segment(A, I) → j
  26. Intersect(i, d) → J
  27. Vector(A, J) → w
  28. Vector(J, I) → k
  29. Angle(J, A, I) → δ
  30. Angle(I, J, A) → ε
  31. Intersect(c, b) → K, L
  32. Segment(A, L) → m
  33. Vector(A, D) → p
  34. Vector(D, L) → q
  35. Angle(L, A, D) → ζ
  36. Angle(A, D, L) → η

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. Mark the intersection of the x-axis and y-axis. Draw a line segment from the origin to a point on the circle. Draw a perpendicular line from the point to the x-axis. Connect the origin to the intersection point of the perpendicular line and the x-axis. Mark all angles formed, including the angle between the hypotenuse and the x-axis, the angle between the perpendicular and the hypotenuse, and the angle between the hypotenuse and the perpendicular.
The prompt above was compiled from the original drawing commands and is for reference only.