# Two arguments arctangent

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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#### Timur

Created: 2018-10-22 11:28:14, Last updated: 2021-03-02 22:03:53

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

atan2 is based on the arctangent function, but it expects two arguments to correctly determine the resulting quadrant.

#### atan2

Digits after the decimal point: 2
Atan2 value on graph
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Result, degrees

### Atan2 calculation algorithm

Arctan2 with all positive x is same as ordinal arc tangent:
$atan2(y,x) = \arctan\frac{y}{x}$, x>0
For other x values, arctan2 can be calculated according the following table:

y<0 y = 0 y>0
x<0 $\arctan\frac{y}{x}-\pi$ $\arctan\frac{y}{x}+\pi$ $\arctan\frac{y}{x}+\pi$
x=0 $- \frac{\pi}{2}$ undefined $\frac{\pi}{2}$
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