# What is difference between atan and atan2 ?

In almost every programming language there some sort of math module with various trigonometric functions including functions called atan and atan2.

#### atan(x,y)

Now everybody knows atan, it’s just inverse tangent, arctan, just as we know it in math. If we have vector v with coordintes [x,y], and we calcualte atan(x,y), we cannot really tell in which quadrant the vector v is in. Absolute value of this result just tells us the smallest angle between the vector v and X-axis.

#### atan2

Atan2 is nothing else just more comfortable version for atan. Result of atan2 returns angle between vector v from the “angular start” on unit circle.

#### Picture is worth thousand words

Compare what angles in radians is returned by atan(x,y) compared to atan2(x,y)

Here, calculating atan(x,y) would result in value approximately around -pi/6 showed on the picture as angle alpha.

In this case, calcualting atan2(x,y) would result in value around 5pi/6, showed on the picture as angle alpha.