Unit Circle and Sine Wave

Overview

An animation that visualizes the relationship between circular motion and the sine function. A point travels counter‑clockwise around a unit circle on the left side of the screen while its vertical coordinate is simultaneously plotted as a sine wave on the right side. The key takeaway is that the sine of an angle equals the y‑coordinate of a point on the unit circle.

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Phases

#	Phase Name	Duration	Description
1	Intro	~2s	The unit circle appears on the left, the empty sine‑wave axis appears on the right, and a highlighted point is placed at $(1,0)$ with a thin line connecting the point to the horizontal axis.
2	Trace	~8s	The point moves smoothly counter‑clockwise around the circle completing one full revolution. As it moves, a dot on the sine‑wave axis rises and falls, tracing the sine curve in real time. A faint trailing line follows the point on the circle, and the corresponding segment of the sine wave is highlighted.

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Layout

┌───────────────────────────────────────────────────────┐
│                                                       │
│  LEFT: Unit circle with moving point                  │
│  RIGHT: Horizontal axis with growing sine trace       │
│                                                       │
├───────────────────────────────────────────────────────┤
│  Caption: "θ → sin(θ)" (small persistent label)      │
└───────────────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	Left side: unit circle of radius 1 centered at the origin; a moving point on its circumference with a radius line. Right side: horizontal axis representing angle (or time) with the sine curve being drawn as the point moves.	Both sub‑visuals share the same time base; the right side expands horizontally as the trace grows.
Caption	Short label "θ → sin(θ)" placed in the bottom band.	Optional; provides a quick reminder of the mapping.

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Notes

• Assumptions: total animation length ~10 seconds, one full circle corresponds to one period of the sine wave; the angle increases linearly with time.
• The caption is optional and can be omitted if a cleaner look is preferred.
• No additional text or equations are displayed during the animation; the visual relationship is conveyed solely by the motion and the traced curve.
• The scene will be implemented as a single Manim Scene class.