Unit Circle and Reference Triangle: Visualizing Trigonometric Functions

This GeoGebra example demonstrates the geometric definition of trigonometric functions (sine, cosine, tangent) using a dynamic point on the unit circle and its associated reference triangle. The core mathematical concepts include the unit circle, angle measurement, right-triangle side ratios, and the periodic nature of trigonometric functions. Construction details: the Circle command creates the unit circle, a Point moves on the circle, Ray and Line establish coordinate axes and reference lines, OrthogonalLine constructs perpendiculars to form the right triangle, Polygon draws the reference triangle, Angle labels α, β, γ, CircleSector and CircleArc visualize sectors and arcs, Intersect finds key points, and a slider (implied) controls the point's position. Suitable for high school trigonometry lessons, college precalculus review, and dynamic demonstrations linking geometry and algebra. By dragging the point, learners observe how the triangle's shape and function values change with the angle, fostering an intuitive grasp of trigonometric relationships.