Dynamic Transformation of the Sine Function y=Asin(ωx+φ)

This example provides an interactive demonstration of the transformations of the sine function y=Asin(ωx+φ). It focuses on the core mathematical concepts of amplitude (A), angular frequency (ω), and initial phase (φ), illustrating how these parameters control vertical stretching, horizontal compression, and phase shifting. The construction utilizes GeoGebra commands such as Point, Circle, Rotate, and Angle, employing auxiliary circles and rotating points (P, Q) to visually map trigonometric values to geometric motion. This tool is ideal for high school mathematics education to help students visualize the relationship between algebraic expressions and their corresponding graphs.