Trig Graphs and the Unit Circle: Dynamic Visualization

①This GeoGebra example dynamically illustrates the correspondence between trigonometric function graphs (sine, cosine, etc.) and coordinates of points on the unit circle, showing how function values are generated as angles change. ②Core mathematical concepts include the unit circle definition of trigonometric functions, periodicity, function graph transformations (rotation, dilation), and piecewise functions for angle intervals. ③Construction highlights: uses commands such as Intersect, Segment, Rotate, Angle, OrthogonalLine, Distance, and Textfield; objects include circle c, points A/B/C, function f, angle β, segments CD/BD, and input boxes, building a complete mapping from the unit circle to function graphs. ④Suitable for high school and early college students learning trigonometry and function graphing, as well as for classroom demonstrations to deepen understanding of the geometric essence and transformation rules of trigonometric functions.