# Two argument arc tangent

The calculator gives an angle between positive axis x and the ray to the given point from point 0. The result corresponds to atan2 function, implemented in many computer languages and math libraries.

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Some math problems, e.g. complex number argument, require to calculate the angle between the ray to the given point and positive x semi-axis. To solve this task many computer languages, e.g. javascript, have atan2 (two argument arc tangent) function. Atan2 returns angle in the range (-π, π] in contrast to ordinal arc tangent, which result is in -π/2 .. π/2.

atan2 is based on arc tangent function, but it expects two arguments to correctly determine the result quadrant.

### Atan2 calculation algorithm

Arctan2 with all positive x is same as ordinal arc tangent:

, x>0

For other x values, arctan2 can be calculated according the following table:

y<0 | y = 0 | y>0 | |
---|---|---|---|

x<0 | |||

x=0 | undefined |

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