Trigonometric Ratios: Geometric Intuition and Construction

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2018-09-07 09:15

This example demonstrates the dynamic changes of trigonometric ratios through geometric figures, helping students understand the core relationships of sine, cosine, and tangent. The construction involves using GeoGebra commands like Intersect, Point, Segment, and Rotate, along with angle and orthogonal line operations to build triangles and related shapes. Suitable for middle or high school mathematics courses to provide a visual foundation for trigonometric concepts.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
Point(xAxis) → C
Segment(A, C) → Adj
Rotate(C, α, A) → C'
Angle(C, A, C') → β
Line(A, C') → a
OrthogonalLine(C, xAxis) → c
Intersect(a, c) → B
Distance(A, B) → AB
Segment(A, B) → Hyp
Segment(C, B) → Opp
Segment(A, C) → f
Angle(B, C, A) → γ