Anne Fibian Rides Paddle Wheel: Unwrapping a Circle to Generate Sine and Cosine

This interactive applet visualizes the classic "unwrapping" construction in which a point on a rotating circle traces out the sine and cosine curves. By rotating a paddle‑wheel‑like mechanism around a unit circle, the horizontal and vertical coordinates of the moving point generate parametric equations x = cos θ, y = sin θ, which are then unwrapped into the familiar sinusoidal graphs. The GeoGebra model uses the Rotate command with objects such as pic1, A, C, and a slider α to control the angle, producing a series of traced points G1–G14 and H1–H14 that form the curves. Core mathematical ideas include trigonometric functions, the unit circle, parametric representation, and the relationship between circular motion and wave forms. This example is ideal for high‑school or early‑college students studying trigonometry, pre‑calculus, or geometry, and serves as a dynamic illustration for classroom demonstrations or online tutorials.