Direction Angle Illustrator: Dynamic Vector & Trigonometry Exploration

① This interactive GeoGebra example dynamically illustrates the concept of direction angle—the angle between a vector and the positive x-axis—with a key question to prompt deeper understanding. ② Core mathematical concepts include angles, trigonometric functions (sine), vectors, right triangles, symmetry, and indefinite integrals, bridging geometry and algebra. ③ Construction details: using GeoGebra commands such as Ray, Rotate, Point, Vector, and Angle, the objects A, B_1, f, a, A', B', f', C, B, u, v, α, and text1 are created to visualize the direction angle through rotation and vector operations. ④ Suitable for high school to early college students, this resource serves as a classroom demonstration or self-study tool for geometry, trigonometry, and vector lessons, and can inspire teachers to build similar interactive materials.