Unit Circle and Trigonometric Function Lines Dynamic Demo

This GeoGebra example constructs a unit circle (radius 1) and dynamically illustrates how the six trigonometric functions—sine (ημ), cosine (συν), tangent (εφ), cotangent (σφ), secant (τεμ), and cosecant (στεμ)—are represented geometrically as line segments on the circle as angle θ varies. Core mathematical concepts include the unit circle definition of trigonometric functions, trigonometric line segments (sine line, cosine line, tangent line, etc.), angle-radian conversion, and periodicity. Construction highlights: the Circle command creates the unit circle, Point and Intersect define a moving point on the circle, Rotate applies angle θ, Angle labels the angle, OrthogonalLine and Line build perpendiculars and auxiliary lines, Segment connects relevant points, Tangent draws tangent lines, and If controls conditional display of different function lines. A slider animates the angle. This resource is ideal for high school or introductory college students learning trigonometry, and for teachers demonstrating the geometric meaning of sine, cosine, and tangent values on the unit circle.