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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.

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 on the graph
Atan2 on the graph

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



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

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}