Sine and Cosine Functions Linked to the Unit Circle

This GeoGebra example demonstrates how a moving point on the unit circle generates the sine and cosine function curves, visually linking circular motion to trigonometric graphs. Core concepts include the unit-circle definition of sine and cosine, the relationship between the central angle α and coordinates (cos α, sin α), the Pythagorean identity x² + y² = 1, and dynamic function graphing. The construction uses GeoGebra commands such as Circle to draw the unit circle, Point to place a movable point, Angle to mark α, Intersect to find intersections, Line and Segment to draw radii and projections, OrthogonalLine to drop perpendiculars to the axes, Distance to measure lengths, and objects SINECURVE and COSCURVE to plot the corresponding curves. It is ideal for high school mathematics (trigonometry unit), classroom demonstrations, inquiry-based learning, and review sessions connecting geometric construction with function graphing.