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.

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 on the graph
Atan2 on the graph

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



Digits after the decimal point: 2
Atan2 value on graph
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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}
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PLANETCALC, Two arguments arctangent