# atan2 ( y ; x )

returns the base angle (arctan) of a triangle with the sides X and Y.

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Michael George Consulting |

1 0

1 1

0 1

-1 1

-1 0

-1 -1

0 -1

1 -1

0

0.7853...

1.5707...

2.3561...

3.1415...

3.9269...

4.7123...

5.4977...

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

The function atan2(y;x) returns the arctan of y,x with adjustments for the signs of x and y so that the angle returned is the angle of the cartesian point (x,y) in radians.

The commonest use of atan2 is in converting between rectangular and polar co-ordinates. The formula for calculating the *initial* heading for a great-circle route from point A to point B uses atan2.

Please be aware that the parameter order is y,x and not x,y as usual.

## Comments

Rouel Fernandez, Mountain View, Ca Dec 22, 2010 |
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The above does not give the same results as Microsoft Excel. I use the following, Note the special for x=0 and y=0, I define ATAN2(x,y) = 0: Let ( [ a = Case ( x > 0 ; Atan( y / x ) ; x < 0 ; If ( y ≥ 0 ; Pi + Atan ( y / x) ; -Pi + Atan ( y / x)) ; x = 0 ; If ( y > 0 ; Pi / 2 ; If ( y < 0 ; -Pi / 2 ; 0) )) ; result =a ]; result ) Convert from 0 to 2*pi: result = mod ( 2* pi + a ; 2 * pi) |
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Michael George, Michael George Consulting Sep 28, 2013 |
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Excel has the two parameters reversed: http://en.wikipedia.org/wiki/Atan2#Variations |
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