I'm struggling to find the cosets of $\langle\mathbb{R}, +\rangle / \langle 360\mathbb{Z}, +\rangle$.
Usually I only find cosets of finite groups, in which case I know the cardinality of the subset and then divide the groups cardinality by that to get the number of cosets. Then it is just a matter of finding what elements are in the other cosets.
But I can't figure out what it is for the infinite sets above. How many cosets are there and how do you know? At the very least, I can imagine the subgroup would be $\{0, 360, 720, ...\}$ (because it has to be a subgroup and have the identity).