# return any angle to (0 to 2pi) range

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Osama Al-Kurdi on 18 Feb 2020
Commented: James Tursa on 19 Feb 2020
I have a cetain angle let us say x
and I want matlab to change x to become within 0 and 2pi range
example: if x=3pi
then the new value of x have to be pi

James Tursa on 18 Feb 2020
Edited: James Tursa on 18 Feb 2020
mod(x,2*pi)
The long answer for this particular mod operation, is that if you want to get the same answer for trig calculations for large inputs that MATLAB does, you need to do the mod differently:
atan2(sin(x),cos(x)); % effectively mod(x,2*pi)
E.g.,
>> x = 10
x =
10
>> y = mod(x,2*pi)
y =
3.716814692820414
>> sin(x)
ans =
-0.544021110889370
>> sin(y)
ans =
-0.544021110889370
>> x = 1e25
x =
1.000000000000000e+25
>> y = mod(x,2*pi)
y =
0
>> sin(x)
ans =
-0.305257800135130
>> sin(y)
ans =
0
>> z = atan2(sin(x),cos(x))
z =
-0.310209139287907
>> sin(z)
ans =
-0.305257800135130
Using the atan2( ) approach to doing the mod(x,2*pi) operation results in effectively the same angle that MATLAB uses for the trig operations.

Osama Al-Kurdi on 18 Feb 2020
how is the remain of the division of 2pi is what I was looking for?
can you explain it?
James Tursa on 19 Feb 2020
I don't understand your question. The remainder of the division is the result of the mod operation.