You are correct that a cyclic compound with only one functional group does not have cis or trans isomers.
It doesn't matter where the functional groups are, just the relationship between their geometries. You can even refer to groups as cis or trans when you have more than two groups, you just have to make it clear which groups you are talking about. This is where the naming gets a little muddy. Suppose you have 1,2,3-trimethyl-cyclopentane. Then suppose that the methyls at 1 and 2 are cis to one another, but the ones at 2 and 3 are trans to one another. You can say that 1 and 3 are trans or whatever, but naming this compounds can be confusing. The correct way to name a compound like that is to use the (R) and (S) configurations of the stereocenters. This gets more confusing when the material is racemic though. The naming conventions aren't really perfect.
BTW, this is a little off topic, but in my example the methyl group at the 2 position is actually not a chiral center. It is what is called a "chirotopic" carbon. I guarantee that you don't need to know that for your class though.