Further Transformations of Sine Functions

This example demonstrates how to analyze the graphs of sine functions by adjusting parameters for amplitude, period, phase shift, and vertical displacement. It focuses on the general form y = A sin(B(x ‑ C)) + D, explaining how each parameter influences the shape, position, and scale of the sinusoidal curve. Using GeoGebra’s Function command, the construction creates dynamic sine curves and employs slider objects (a, b, c, d, etc.) to control amplitude, frequency, phase, and vertical shift in real time. Key points such as peaks, valleys, and transformation markers (T1‑T8) are plotted to illustrate the effects of each parameter. The interactive nature of the sliders allows students to explore how changes in amplitude affect height, how period adjustments alter wavelength, how phase shift moves the graph horizontally, and how vertical displacement lifts or lowers the entire curve. Designed for high‑school and early‑university mathematics courses, the example serves teachers and learners seeking an exploratory tool to understand trigonometric function transformations. It supports curriculum goals in function graphing, trigonometric identities, and geometric transformations, providing a hands‑on approach to mastering sine function behavior.