Point on Unit Circle with Corresponding 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, while its vertical coordinate is simultaneously plotted as a sine wave on the right. 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 axis appears on the right, and a point at $(1,0)$ is highlighted.
2	Rotation & Tracing	~8s	The point moves smoothly around the circle completing one full revolution. As it moves, a vertical line drops from the point to the horizontal axis, and the tip of that line draws the sine wave on the right in real time.
3	Highlight & End	~2s	After the full cycle, the completed sine wave is emphasized, the point returns to the start, and a brief label $y = \sin\ heta$ fades in near the wave.

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Layout

┌───────────────────────┬───────────────────────┐
│                       │                       │
│      MAIN LEFT        │      MAIN RIGHT       │
│   (unit circle)       │   (sine axis)         │
│                       │                       │
├───────────────────────┴───────────────────────┤
│ Caption / label (optional, small text)      │
└───────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main Left	Unit circle of radius 1 centered at the origin, with a moving point and a radial line indicating the current angle $\ heta$.	Primary visual for circular motion
Main Right	Horizontal axis representing angle (or time) and vertical axis for sine value; the sine curve is drawn progressively as the point moves.	Mirrors the left side in real time
Caption	Optional brief text such as "$y = \sin\ heta$" that appears at the end.	Can be omitted if not needed

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Notes

• Assumptions: The animation runs for a single period (0 → $2\pi$), uses a smooth linear speed, and the sine axis is scaled to fit one wavelength horizontally.
• The total runtime is kept under 12 seconds to stay well within the 30‑second guideline.
• No persistent on‑screen text is used except the final optional label, adhering to the “avoid text unless necessary” rule.
• The scene will be implemented as a single Manim Scene class.
• All transitions are simple fades or linear motions; no complex effects are required.