# Visual Inverse Trig and atan2 Without Math Libraries
Canonical public lesson for finding an angle from a point.
## One picture
Given a point `(x, y)`, draw an arrow from the origin to the point. The angle `θ` is measured from the positive x-axis.
## Simple idea
Regular trig asks: angle → point.
Inverse trig asks: point → angle.
## Right triangle view
```text
rise = y
run = x
slope = y / x
angle = atan(y / x)
```
## Why atan2 exists
`atan(y/x)` loses quadrant information.
`atan2(y, x)` uses both signs:
- `x > 0, y > 0`: quadrant I
- `x < 0, y > 0`: quadrant II
- `x < 0, y < 0`: quadrant III
- `x > 0, y < 0`: quadrant IV
## No-library implementation ideas
- Use a lookup table of slopes to angles.
- Interpolate between nearby slope values.
- Add quadrant correction based on signs of `x` and `y`.
Source task: `49bd7500-609e-47d9-afa9-a6eee820c8a8`