Extending Trigonometric Function Domains with Geometric Construction

This GeoGebra practice demonstrates how to extend the domain of trigonometric functions beyond their basic range by using geometric construction and intersection points. It highlights the piecewise nature that appears when angles correspond to different geometric configurations, making the mapping from angle/location to function value visible. Key concepts include domain extension for trigonometric functions, angles represented geometrically, and the idea behind piecewise functions as different rules apply on different intervals. Construction-wise, the provided command summary shows the use of Intersect and Line: several lines are drawn (Line) and intersected (Intersect) to locate critical points (e.g., objects such as A, B, C, B', D–G, H–L and parameter/angle-related items like α and β). Those intersections serve as anchors for building the function-related objects that depict the extended behavior. Suitable for high-school learners and classroom demonstrations linking geometry constructions with function/graph understanding.