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True Meanings of the 3 Trigonometric Ratios

True Meanings of the 3 Trigonometric Ratios
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2015-11-14 01:18
AngleTrigonometryGeometric Construction
In collections GA Chapter 8: Right Triangles and Trigonometry Geometry Applets
This example demonstrates the true meanings of sine, cosine, and tangent within a right triangle context. It involves core math concepts like trigonometric definitions, right triangle properties, and angle measurement. Construction highlights include using GeoGebra commands such as Segment, OrthogonalLine, Point, Ray, Angle, Rotate, Polygon, Midpoint, and Vector. Suitable for middle school and above students to understand practical applications and geometric interpretations of trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → E
  4. Ray(B, E) → c
  5. Angle(A, B, E) → α
  6. Point(c) → C
  7. Segment(C, A) → d
  8. Angle(B, C, A) → β
  9. Segment(B, C) → e
  10. Rotate(B, If[0 < f ≤ 1, (f * β), 0], C) → B'
  11. Rotate(C, If[0 < f ≤ 1, (f * β), 0], C) → C'
  12. Segment(B', C') → e'
  13. Angle(C, A, B) → γ
  14. Rotate(A, If[0 < g ≤ 1, ((-g) * γ), 0], A) → A'
  15. Rotate(B, If[0 < g ≤ 1, ((-g) * γ), 0], A) → B'_1
  16. Segment(A', B'_1) → a'
  17. Rotate(B, If[0 < h ≤ 1, ((-h) * α), 0], B) → B'_2
  18. Rotate(C, If[0 < h ≤ 1, ((-h) * α), 0], B) → C'_1
  19. Segment(B'_2, C'_1) → e'_1
  20. Polygon(B, A, C) → poly1, c_1, b_1, a_1
  21. Midpoint(e') → D
  22. Vector(F, D) → u
  23. Midpoint(a') → G
  24. Vector(H, G) → v
  25. Midpoint(e'_1) → I
  26. Vector(J, I) → w