Visual Link Between the Unit Circle and Sinusoidal Graphs

This example demonstrates how a point moving on the unit circle as an angle varies can be linked to the corresponding sinusoidal wave: the vertical projection of the rotating point gives sin(θ). The key mathematics includes the unit circle, right-triangle trigonometric meaning of sine, angle measurement, and interpreting a function graph through geometry (including period and symmetry). Construction-wise, it uses GeoGebra commands Circle to build the unit circle, Angle to define the rotation angle α from a reference direction, and Segment to form connecting lines that create the right-triangle structure and the coordinate projection. The scene is annotated with text objects (e.g., text1–text7, α) and controlled via interactive buttons (button1–button4) to vary θ and update the graph correspondence. Suitable for high school through early college, for introducing trigonometry and helping students connect formulas to geometric intuition.