Question

How could I get the angle in Degree from 0 to 360 from Cartesian coordinate such that :

{1,0}  = 0   Degree
{0,1}  = 90  Degrees
{-1,0} = 180 Degrees
{0,-1} = 270 Degrees

I am having a hard Time with ArcTan to get the angle bet 180 to 359…

Answer 1

Try:

f[x_List] := Mod[ArcTan @@ x /Pi 180 Degree, 360 Degree]

f /@ {{0, -1}, {0, 1}, {1, 0}, {-1, 0}}
(*
 -> {270 \[Degree], 90 \[Degree], 0, 180 \[Degree]}
*)

Edit

As the previous form was criticized upon, here is another way to do the same. Not so easy to follow for my taste:

f = (180 /Pi ArcTan @@ #)~Mod~360 &