Point on Unit Circle and Corresponding Sine Wave

Overview

A point travels counter‑clockwise around a unit circle while its vertical coordinate is simultaneously plotted as a sine wave on the right. The animation visualizes the geometric relationship between circular motion and the sine function.

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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 label "$y = \sin\ heta$" fades in.
2	Motion	~8s	A point starts at $(1,0)$ and moves smoothly around the circle. A vertical line from the point to the horizontal axis follows its projection, and the tip of the line draws the sine wave on the right in real time.
3	Outro	~2s	The point and the traced sine wave pause, then both fade out, leaving only the completed sine curve and a brief caption "Circular motion ↔ sine wave" at the bottom.

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Layout

┌───────────────────────────────────────┐
│               TOP AREA                 │
├───────────────────────┬───────────────┤
│                       │               │
│      LEFT AREA        │   RIGHT AREA  │
│  (unit circle +      │ (sine axis &  │
│   moving point)      │   traced wave)│
│                       │               │
├───────────────────────┴───────────────┤
│               BOTTOM AREA              │
│   Caption / small notes (optional)    │
└───────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title: "Circular Motion → Sine Wave"	Fades in with the intro phase
Left	Unit circle of radius 1 centered at the origin, a moving point $P$ and a vertical projection line	Primary visual; point moves at constant angular speed
Right	Horizontal axis for time (or angle) and vertical axis for amplitude, the sine curve being drawn in real time	The curve starts empty and is traced as the point moves
Bottom	Small caption "Circular motion ↔ sine wave" that appears in the outro	Appears only in the final 2 seconds

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Notes

• The angular speed is chosen so that one full revolution (2π radians) corresponds to the full width of the sine axis, keeping the total motion under 10 seconds.
• The vertical projection line helps viewers see that the y‑coordinate of the point equals the sine value being plotted.
• All elements fade in/out smoothly (0.5 s cross‑fade) to keep the animation fluid.
• No textual labels are placed on the axes beyond the brief title; the visual relationship is conveyed purely by motion.