Dynamic Representation of Arbitrary Angles

This GeoGebra example dynamically illustrates arbitrary angles—including those exceeding 360° or negative angles—in standard position on the Cartesian plane, showing how their terminal sides rotate around the origin. It covers core mathematical concepts such as radian and degree measures, trigonometric definitions via the unit circle, parametric curves, and geometric relationships among vectors, rays, and angles. The construction uses commands like Circle and Point to create the unit circle and a moving point; Angle, Ray, and Vector to define the angle and its orientation; CurveCartesian with a parameter (param) to trace the locus of the terminal side; and Mod for angle normalization. Additional elements like Intersect, Segment, and CircleArc label key points and arcs. Ideal for high school trigonometry instruction or pre-university coordinate geometry, this tool helps learners visualize the periodicity, quadrant placement, and rotational nature of arbitrary angles.