Multiplicative 3: Angles and Ratios on the Unit Circle

This GeoGebra example dynamically illustrates multiplicative relationships through geometric constructions on the unit circle, connecting angles, ratios, and trigonometric functions. The core mathematical concepts include tangent function, coordinate geometry, ratios, congruence, and geometric distribution. The construction uses commands such as Vector, Circle, Point, Rotate, Angle, CircleSector, and CircleArc, with objects including points B, C, D, F, E, G, H, K, L, M, N, O, P, Q and lines/segments a, b, c, d, e, f, g, h, u, v, w. It visualizes how rotating vectors and measuring angles produce proportional relationships, making it suitable for high school or early college students studying trigonometry and geometric transformations. Teachers can use it as an interactive demonstration to explore the interplay between angles, coordinates, and multiplicative scaling.