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Exploring Trig Ratios by Patrick Cobb

Exploring Trig Ratios by Patrick Cobb
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2015-02-23 17:51
AngleTrigonometryGeometric Construction
This example demonstrates the effect of changing the angle and triangle size on the ratios of the sides by investigating trigonometric ratios (sine, cosine, tangent). It involves core math concepts like trigonometry and geometric constructions using commands such as Intersect, Point, Rotate, Angle, Line, OrthogonalLine, and Segment in GeoGebra. Suitable for high school mathematics education or self-learning to understand the relationship between trigonometric functions and geometric properties of triangles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → β
  5. Line(B', A) → a
  6. OrthogonalLine(B, xAxis) → b
  7. Intersect(a, b) → C
  8. Segment(A, B) → c
  9. Segment(B, C) → d
  10. Segment(C, A) → e
  11. Angle(C, B, A) → γ

AI Drawing Prompt Reference

Draw a right triangle ABC with A at the origin, B on the x-axis, and C as the right angle vertex. Rotate point B around A to form point B', measure the angle ∠BAB' as β, draw a line a through B' and A, draw a perpendicular line b from B to the x-axis, and find the intersection C of lines a and b. Measure the angle ∠CBA as γ, and measure the lengths of AB, BC, and CA to observe the relationship between the sides and angles of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.