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Values of Trigonometric Ratios in Different Quadrants

Values of Trigonometric Ratios in Different Quadrants
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2016-03-28 21:19
AngleTrigonometryGeometric Construction
This example demonstrates how the signs and values of trigonometric ratios (sine, cosine, tangent) change as the angle moves through different quadrants. Using commands like Circle, Point, Tangent, Rotate, Line, Intersect, Angle, Segment, and OrthogonalLine, students can visually understand the behavior of trigonometric ratios. Suitable for middle school and above students learning trigonometry.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Tangent(B, c) → a_2,
  4. Rotate(B, β, A) → C
  5. Line(A, C) → b
  6. Intersect(a_2, b) → D
  7. Angle(B, A, C) → α
  8. Segment(B, D) → f
  9. OrthogonalLine(C, xAxis) → g
  10. OrthogonalLine(C, yAxis) → h
  11. Intersect(h, yAxis) → F
  12. Intersect(g, xAxis) → H
  13. Segment(F, C) → i
  14. Segment(C, H) → j
  15. Segment(A, F) → k
  16. Segment(A, H) → l
  17. Point(c) → J
  18. Tangent(J, c) → m,
  19. Line(A, C) → d
  20. Tangent(J, c) → e,
  21. Intersect(e, d) → E
  22. Segment(E, C) → p
  23. Segment(C, A) → q
  24. Segment(J, E) → r
  25. Tangent(C, c) → s,
  26. Intersect(yAxis, s) → G
  27. Segment(C, G) → t
  28. Segment(A, G) → a_1
  29. Tangent(C, c) → b_1,
  30. Intersect(b_1, xAxis) → I
  31. Segment(C, I) → c_1
  32. Segment(A, I) → d_1
  33. Segment(C, D) → e_1