# How do I choose only one branch of ArcTan? [closed]

I have a problem concerning ArcTan drawing a graph using ListPlot. I import a table of data:

a = Import["D:\2_b=10a.txt", "Table"];


Then I write:

ListPlot[Table[{i*0.005 Pi, -ArcTan[(a[[i]][] -
a[[i - 1]][]), (a[[i]][] - a[[i - 1]][])]}, {i, 2, 401, 1}]], PlotRange -> {{0, Pi}, {-4, 4}}]


The returned graph looks like I know from the nature of my calculations that the function must be continuous on the interval $[0,Pi]$, but at $3Pi/4$ the ArcTan function goes to another branch, since ArcTan[x,y] chooses a quadrant. How could I possibly try to move the bottom part of the plot up by Pi, so the function is smooth and continuous?

I tried defining a function

myArcTan[x_] := Piecewise[{{ArcTan[x] + Pi, x < 0}, {ArcTan[x], x > 0}}];


but it doesn't work. Thank you very much.

• This or this might help. – Daniel Lichtblau Aug 14 '14 at 17:42
• Please upload your data or provide a self-contained example. – Mr.Wizard Aug 14 '14 at 20:37