Unit Circle Sine And Cosine Projections
An angle sweeps around the unit circle from 0 to 2 pi while a radius arm rotates. Vertical and horizontal projections trace out sine and cosine values in real time, showing how both functions emerge from the same rotating point. The Pythagorean identity sin^2 + cos^2 = 1 stays visible, linking the circle's radius to the trigonometric relationship. Useful for students first learning how sine and cosine are defined geometrically.
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The prompt that made it
Show the unit circle with sin and cos as projections while the angle sweeps from 0 to 2pi, with a title and the identity sin^2 + cos^2 = 1
Make the next one in this series
- Animate sine and cosine graphs being traced out alongside the unit circle sweep
- Show tangent as a projection using a tangent line touching the unit circle
- Illustrate how the identity extends to sin(2theta) and cos(2theta) using double angle geometry
