June 16, 2018

3 min read

The inverse tangent function, `Math.atan()`

, is useful to calculate the angle of a provided ratio of a sides of a triangle (like a velocity vector's `x`

and `y`

values). This can be useful to find the angle an object should be rotated to face in the direction it's moving, `Math.atan(velocity.y/velocity.x)`

.

The normal arctangent function has a couple issues though for this use case:

- In other programming languages, dividing by zero will cause an error if the x value of the vector (when moving horizontally). In JavaScript, this division returns the
`Inifinity`

number which`Math.atan()`

can actually handle correctly. - The arctangent function's domain is -π/2 to π/2 radians (-90° to 90°). This means it cannot distinguish between
`{x: 1, y: 1}`

and`{x: -1, y: -1}`

.`Math.atan(y/x)`

both evalute to 0.785 radians (45°).

This is where the arctangent2 function comes in handy. `Math.atan2(y, x)`

functions the same way as the `Math.atan(y/x)`

function with a special exception. This function has a domain of -π to π radians (-180° to 180°). Revisiting the earlier example, `{x: 1, y: 1}`

and `{x: -1, y: -1}`

evaluate to 0.785 radians (45°) and -2.356 radians (-135°) respectively. This allows you to correctly orient an object to any velocity vector in a circle.

#examples

```
// Returns an angle in degrees representing the facing of an object with the given velocityfunction convertVelocityToAngle(velocity) { const { x, y } = velocity;
return Math.atan2(y, x) * (180 / Math.PI);}
```

#sources

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/atan2 https://gamedev.stackexchange.com/questions/14602/what-are-atan-and-atan2-used-for-in-games