The Unit Circle: Interactive Trigonometric and Geometric Construction

This GeoGebra example dynamically illustrates the fundamental properties of the unit circle, showing how coordinates of points on the circle correspond to angles and trigonometric values. Core mathematical concepts include the unit circle definition, angle rotation, geometric meaning of sine and cosine, and connections with polygons, segments, and other basic geometric elements. Construction highlights: the Circle command creates the unit circle, Intersect finds key points, Rotate and Angle build rotation angles, OrthogonalLine constructs perpendiculars, Polygon forms related triangles, and Textfield/InputBox allow parameter input and dynamic adjustment. Suitable for high school and early college students to grasp the relationship between trigonometry, radian measure, and the unit circle, and also serves as an interactive tool for classroom demonstrations or self-directed exploration.