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Trigonometric Ratios CAST Demonstration

Trigonometric Ratios CAST Demonstration
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2017-05-18 15:46
AngleTrigonometryGeometric ConstructionGraphing
This example demonstrates the application of the CAST rule in trigonometric ratios within any triangle, visually showcasing the relationship between angles and trigonometric values through dynamic interaction; Core math concepts include trigonometric functions (sine, cosine, tangent), angle classification (acute, obtuse), coordinate systems, and unit circles; Construction highlights GeoGebra commands used: Intersect (intersection), Circle (circle), Point (point), DynamicCoordinates (dynamic coordinates), Segment (segment), Angle (angle); Suitable for high school mathematics students and teachers to understand trigonometric properties and geometric significance, enhancing intuitive grasp of the CAST rule.

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