# Visual Unit Circle Sine and Cosine Without Math Libraries
Canonical public lesson for unit circle sine and cosine.
## One picture
Put a point on a circle of radius `1`.
- `cos(θ)` is the point's **x-coordinate**
- `sin(θ)` is the point's **y-coordinate**
```text
point = (cos θ, sin θ)
```
## Simple idea
Cosine is sideways position. Sine is vertical position.
## Key angles
- `0°`: `(1, 0)`
- `90°`: `(0, 1)`
- `180°`: `(-1, 0)`
- `270°`: `(0, -1)`
- `360°`: `(1, 0)`
## No-library implementation ideas
- Use a lookup table for common angles.
- Interpolate between nearby table entries.
- Use symmetry: one quadrant can generate the rest.
```python
# tiny example table
SIN = {0: 0, 90: 1, 180: 0, 270: -1, 360: 0}
COS = {0: 1, 90: 0, 180: -1, 270: 0, 360: 1}
```
Source task: `28edca38-b9c3-4e78-9584-3296198a915f`