The Cosine and the Unit Circle: A Geometric Visualization

This GeoGebra applet provides a dynamic visualization of how the cosine function varies as the central angle changes on the unit circle. The core mathematical concepts covered include the unit circle definition of trigonometric functions, the periodic nature of the cosine wave, and the geometric projection of a rotating point onto the Cartesian axes. Constructed using key GeoGebra commands such as Circle, Segment, OrthogonalLine, Polygon, and Angle, the model builds a robust geometric skeleton. It uses intersection points and auxiliary polygons (like poly1) to map the angular parameter α directly to the cosine curve (cosine). This interactive tool is ideal for high school and introductory college-level trigonometry courses, helping students bridge the gap between geometric definitions and algebraic function graphs through visual, hands-on exploration.