Unit Circle Origin Symmetry: Exploring Cosine Relationship

This GeoGebra applet demonstrates how the origin symmetry of the unit circle relates to the cosine function. Students can drag a point on the unit circle and observe the corresponding cosine value, while also exploring the effect of rotating by π (180°) which yields the opposite cosine due to central symmetry about the origin. Core concepts include the unit circle definition of cosine, periodic behavior, and symmetry transformations. The construction uses Circle, Segment, and Angle commands, with objects such as center O, points A and A' (symmetric about origin), auxiliary points B, B', E, and angle α. This interactive tool is ideal for high school trigonometry, pre-calculus, or introductory calculus courses, especially when discussing integrals over symmetric intervals or the parity of functions.