Identifying equivalence classes with the unit circle

[The1TL]

Homework Statement

Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way?

Homework Equations

The Attempt at a Solution

I have already proven that this is an equivalence relation but i do not understand how the equivalence classes relate to the unit circle

 

[SammyS]

One fairly obvious equivalence relation on the unit circle can be obtained by considering the results of using θ and (2π + θ) as arguments of the trig functions.