Trigonometric Ratios for Specific Angles

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2017-07-31 23:06

This example demonstrates the geometric representation of trigonometric ratios (sine, cosine, tangent) for specific angles (e.g., 30°, 45°, 60°). It involves core concepts like the definition of trigonometric functions, right triangles, and the unit circle. GeoGebra commands such as Intersect, Point, CircleSector, Segment, Rotate, Angle, Line, Circumference, and Distance are used to construct the图形. It is suitable for high school students learning trigonometric properties and can be used in teaching parametric equations and geometric transformations.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
Point(xAxis) → B
Point(yAxis) → C
CircleSector(A, B, C) → c
Segment(A, B) → b
Rotate(B, α, A) → B'
Angle(B, A, B') → β
Line(B', yAxis) → a
Segment(B', A) → d
Intersect(c, a, 1) → D
Segment(A, B) → e
Intersect(a, b) → E
Segment(B', E) → f
Segment(A, E) → g
Angle(D, E, A) → γ
Angle(A, D, E) → δ
Circumference(c) → h
Distance(f, d) → i
Circumference(c) → j
Circumference(c) → k
Distance(A, E) → distanceAE