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Trigonometric Ratios Demo by np2cmath

Trigonometric Ratios Demo by np2cmath
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2015-04-16 11:26
CircleAngleTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the relationships between side lengths and angles in a right triangle, covering core trigonometric concepts, right triangle properties, and angle measurement. It is constructed using GeoGebra commands like Intersect, Circle, Point, DynamicCoordinates, Segment, and Angle, making it suitable for high school mathematics education to understand basic trigonometric principles and practical applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Point(c) → D
  4. DynamicCoordinates(D, If[Distance[D, I] < z, x(I), If[Distance[D, J] < z, x(J), If[Distance[D, K] < z, x(K), x(D)]]], If[Distance[D, I] < z, y(I), If[Distance[D, J] < z, y(J), If[Distance[D, K] < z, y(K), y(D)]]]) → C
  5. Segment(A, C) → a
  6. Angle(xAxis, a) → Θ
  7. Segment(C, E) → b
  8. Point(xAxis) → G
  9. Segment(F, G) → d
  10. Angle(a, d) → α
  11. Point(d) → H
  12. Angle(d, a) → β
  13. Angle(a, xAxis) → γ
  14. Angle(xAxis, a) → δ
  15. Segment(H, E) → e
  16. Point(a) → P
  17. Point(c) → Q
  18. Segment(P, Q) → f
  19. Point(e) → S
  20. Segment(P, R) → g
  21. Segment(R, Q) → h
  22. Angle(xAxis, f) → ε
  23. Angle(xAxis, f) → ζ
  24. Angle(f, xAxis) → η
  25. Angle(Q, P, R) → θ
  26. Angle(R, P, Q) → ι