The Sine Function and the Unit Circle

This interactive GeoGebra example visualizes the geometric relationship between the sine function and the unit circle, demonstrating how the sine value corresponds to the vertical projection of a rotating radius. Core mathematical concepts include the unit circle definition of trigonometric functions, sine function, angle measurement in radians, and function graphing. Construction details: the Circle command creates the unit circle, a Point moves along the circle, a Segment connects the center to the moving point, an Angle marks the rotation, and a Function plots the sine curve. A slider controls the angle, while Intersect, Midpoint, and other commands link the circle's sine segment to the corresponding point on the graph. Suitable for high school and introductory college students learning trigonometry, function transformations, or pre-calculus, and useful for classroom demonstrations or self-exploration of periodicity, amplitude, and phase shifts.