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Exploring Trig Ratios

Exploring Trig Ratios
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2015-12-17 21:36
AngleFunctionTrigonometryGeometric Construction
This example demonstrates how changing the angle and triangle size affects the ratios of the sides, focusing on trigonometric functions. Key math concepts include trigonometric ratios, right triangle side lengths, and function graphs. It is constructed using GeoGebra commands like Intersect, Point, Rotate, Angle, Line, OrthogonalLine, Segment, and Distance, involving objects such as A_1, A_2, β_2, B', β, a, b, C, A, O, H, γ, f, g, etc. Suitable for high school mathematics education to understand the definitions and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Point(xAxis) → A_2
  3. Rotate(A_2, β_2, A_1) → B'
  4. Angle(A_2, A_1, B') → β
  5. Line(B', A_1) → a
  6. OrthogonalLine(A_2, xAxis) → b
  7. Intersect(a, b) → C
  8. Segment(A_1, A_2) → A
  9. Segment(A_2, C) → O
  10. Segment(C, A_1) → H
  11. Angle(C, A_2, A_1) → γ
  12. Distance(A_2, O) → distanceBO