# Changing the atan function so that it ranges from 0 to 2*pi

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KA on 12 Jun 2011
I know that the matlab atan function returns values in the range of -pi/2 to pi/2. How do i change it so that it goes over the full range 0 to 2*pi?
My first attempt was using a while loop, but it was incorrect.
I need to write a function mfile to set the built-in matlab function atan in the range of 0 to 2*pi without using atan2. im new to matlab so im unsure of what to do.
Thank you
##### 2 CommentsShow 1 older commentHide 1 older comment
Stephen23 on 27 Oct 2018
See Daniel Svedbrand's answer for the simplest solution.

Daniel Svedbrand on 14 Sep 2018
Edited: John D'Errico on 3 Aug 2023
Adding mod 2*pi to atan2 should work just fine
z = mod(atan2(y,x),2*pi);
John D'Errico on 3 Aug 2023
Edited to remove profanity in the answer.

Walter Roberson on 12 Jun 2011
KA on 12 Jun 2011
ok, did not know that, thanks again

Paulo Silva on 12 Jun 2011
The Wikipedia got all explained, you just need to do the code, it's very simple.
function v=myatan(y,x)
if nargin==1 %just in case the user only gives the value of y myatan(y)
x=1;
end
v=nan;
if x>0
v=atan(y/x);
end
if y>=0 & x<0
v=pi+atan(y/x);
end
if y<0 & x<0
v=-pi+atan(y/x);
end
if y>0 & x==0
v=pi/2;
end
if y<0 & x==0
v=-pi/2;
end
if v<0
v=v+2*pi;
end
end
##### 2 CommentsShow 1 older commentHide 1 older comment
Mehmet Can Türk on 9 Apr 2022
Edited: Mehmet Can Türk on 9 Apr 2022
I checked the Wikipedia link and tested the code. First of all, thank you so much for the contribution.
I wanted to convert atan2 function from Matlab into another environment which supports only atan function. So I deleted the if block and everything worked perfectly.

Kent Leung on 21 Mar 2018
Edited: Kent Leung on 21 Mar 2018
Better late than never. (Also posting as a future reference to myself.) The function below accepts y & x as vectors in Matlab. Rather than using 'if' statements, the below might be faster if there is some parallelization implemented in the built-in index searching.
Note: I have a slight disagreement with the above for the x>0 & y<0 case, as well as the for x=0 & y<0 case. The code below gives 0 to 2pi.
function v=myatan(y,x)
%---returns an angle in radians between 0 and 2*pi for atan
v=zeros(size(x));
v(x>0 & y>=0) = atan( y(x>0 & y>=0) ./ x(x>0 & y>=0) );
v(x>0 & y<0) = 2*pi+atan( y(x>0 & y<0) ./ x(x>0 & y<0) );
v(x<0 & y>=0) = pi+atan( y(x<0 & y>=0) ./ x(x<0 & y>=0) );
v(x<0 & y<0) = pi+atan( y(x<0 & y<0) ./ x(x<0 & y<0) );
v(x==0 & y>=0) = pi/2;
v(x==0 & y<0) = 3/2*pi;
end
Sharad Keshari on 26 Nov 2020

theodore panagos on 27 Oct 2018
You can use the formula:
atan(x,y)=pi-pi/2*(1+sgn(x))*(1-sgn(y^2))-pi/4*(2+sgn(x))*sgn(y) -sgn(x*y)*atan((abs(x)-abs(y))/(abs(x)+abs(y)))
x=x2-x1 and y=y2-y1
theodore panagos on 6 Aug 2023
atan2(x,y)=pi/2*(1-sign(x))*(1-sgn(y^2))+pi()/4*(2-sgn(x))*sign(y)-sign(x*y)*atan((abs(x)-abs(y))/(abs(x)+abs(y)))

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