The Pulse of a Circle: Visualizing Trigonometry
Connecting the Sine Wave to Circular Motion
Lab Results: The Sinusoidal Projection of Circularity
Most of us learn the Sine Wave as a static squiggle in a textbook. But in the Digital Lab, we treat it as a dynamic record of a journey. By tracking the vertical displacement of a point traveling around a unit circle, the wave isn’t just a shape—it’s a story of rotation over time.
The Mathematical Model
This relationship is a fundamental concept in Trigonometric Projections and is a classic example of Simple Harmonic Motion.
2. The Geometry of the Sine Wave: Mapping the Unit Circle
The vertical displacement, denoted as y, is a function of the rotation angle θ.
As the vector rotates, the height y oscillates between 1.8 and -1.8, creating the wave pattern seen in the animation.
Name: Source Code: Manim Implementation *