Fun Graphs Generated by Trigonometric Parametric Equations

① This applet demonstrates how trigonometric parametric equations generate a variety of intricate and visually engaging plane figures, revealing the connection between algebraic expressions and geometric shapes. ② Core mathematical concepts include trigonometric functions (sine, cosine), parametric equations, geometric transformations (scaling, translation), polygon construction, and locus generation. ③ Construction highlights: Based on the summary, the applet uses GeoGebra commands such as Polygon, Point, and Segment, defining parameters (a, b, c, d, t) and derived objects (at, bt, ct, dt). Sliders (tmin, tmax, button1) control the parameter range, while points A, B, C, D construct polygon poly1, combined with segments and text objects (text2, text21, etc.) to visualize dynamic changes. ④ Suitable for high school or early college students, this applet helps explore parametric equations and trigonometric graphs, and can serve as a tool for mathematical experimentation and inquiry-based learning.