# What is it called when you subtract multiples of 360 degrees?

When you divide a vector by its magnitude to get a unit vector, there's a verb for that: you are "normalizing" the vector.

Similarly, is there a verb for when you subtract multiples of $$360$$ degrees to find a coterminal angle?

E.g., if I start with the angle $$736.4^o$$, and subtract $$720^o$$ to get the coterminal angle $$16.4^o$$, is there a verb for what I just did?

This coterminal angle can be found with the modulo function - $$\text{mod}(736.4,\ 360)\$$- but "modulo-ing" is probably not the verb I'm looking for.

• Some might call this taking the principal value or something similar Apr 1, 2019 at 23:32
• I'd throw in: operating modulo 360 (mod 360). You may also look up "congruence".
– MasB
Apr 1, 2019 at 23:39
• You can say "reducing modulo 360" Apr 2, 2019 at 0:02
• you're using the wrapped version of the angle. In highfalutin language, you're working with equivalence classes of angles modulo 360 degrees (or modulo a full rotation).
– JMJ
Apr 2, 2019 at 1:23

## 1 Answer

I'd be fine with “normalizing”. The general idea of normalization is that you have a definition of what you consider normal (the normal form), and a class of transformations to turn other things to that normal form. For vectors, normal is unit length, and transformations are scaling. For angles, picking 0° − 360° (or −180° − +180°) as normal range, and addition / subtraction of full turns as transformations, makes just as much sense.

I might also call this the “canonical representation” of the angle, but I can't think of a good verb to go with that. To me this terminology has a connotation of equivalence classes lurking in the background, which is quite applicable here.

If you are looking for verbs and don't like normalization, the “reduction modulo 360°” which Jair Taylor wrote in a comment likely allows subsequent usage to only use “reduction” for the operation.