Extending Trigonometric Function Domains via Graphs

This example demonstrates how extending the domain settings for trigonometric functions can be visualized through graphs, helping learners understand how sine/cosine relationships remain consistent while the representable input interval changes. Key ideas include domain and range of trigonometric functions, the role of the unit-circle/coordinate correspondence in establishing values, and the periodic nature of trigonometric functions. The construction in practice focuses on plotting the trigonometric function(s) on the coordinate plane and comparing the curve behavior when the x-domain is broadened, emphasizing how points map correctly and the periodic pattern is preserved. The provided construction summary is empty, so the essential GeoGebra elements are the function objects and their graphing on a 2D coordinate system. Suitable for middle-to-high school students studying functions and trigonometry, and for classroom demonstrations or self-learning to build intuition about domain extension using visual evidence.