Dynamic Definition of Trigonometric Ratios for Arbitrary Angles

This interactive GeoGebra example dynamically demonstrates how the trigonometric ratios (sine, cosine, tangent) of an arbitrary angle are defined by the coordinates of a moving point P on its terminal side relative to the origin. The core mathematical concepts include the definition of trigonometric ratios for any angle, the relationship between coordinates (x, y) and radius r, and the sign conventions across quadrants. The construction utilizes GeoGebra commands such as Rotate, Sequence, Point, Angle, Circle, Segment, Vector, and If to create the dynamic visualization and algebraic displays. It is designed for high school mathematics educators and students to visually grasp the geometric essence of arbitrary angle trigonometry.