Sine and cosine are the unit circle's shadows
A point travels around the unit circle while its vertical and horizontal coordinates are tracked in real time. As the angle sweeps from 0 to 2π, these coordinates are plotted alongside the circle, unrolling into the familiar sine and cosine waves. The animation makes clear why these functions are periodic and how their values connect directly to circular motion. Useful for students first learning trigonometric functions and the geometric meaning behind their graphs.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
A point moves around the unit circle. Its height is sin θ and its horizontal position is cos θ. As the angle sweeps from 0 to 2π, plotting those two lengths against the angle traces the sine and cosine waves side by side.
Make the next one in this series
- Show how tangent relates to the slope of the line from the origin to the moving point
- Animate phase shifts by starting the point at different initial angles
- Compare unit circle motion to a mass on a spring undergoing simple harmonic motion
