Geometric construction of the sine function sun(x) using a circle

This GeoGebra example demonstrates how the sine function (denoted as sun(x)) emerges from a circle-based geometric relationship, linking a rotating angle to the corresponding length/projection that varies periodically. It centers on core ideas of trigonometry: the sine function, periodicity, and the interpretation of trigonometric values via unit-circle (or circle) geometry, connecting geometric projections to a function graph. Construction-wise, the setup uses GeoGebra commands such as Function and Circle to define the function behavior and create the circular geometry, while multiple parameter objects (e.g., A, a, B, amp, w, b, c, f, p, t, C, d, e, g, and texte1) control inputs like angle, amplitude, and frequency. The inclusion of Animation and labeling (texte1) supports an interactive/animated view of how changing parameters updates the sine-related geometry. Suitable for middle/high school trigonometry lessons, function graphing comprehension, and classroom activities emphasizing geometric intuition.