@ AWK: agreed.
cis/trans is generally reserved for geometry about a double bond, and sometimes for relative positions in a cyclic system. syn/anti is also generally used for relative positions in a cyclic systems, but it can also be used for net creation of 2 new stereocenters.
And you are correct, you form a racemic mixture of two products, and both will be formed in equal amounts.
I didn't check your r/s nomenclature, but assuming you prioritized each substituent correctly, then a job very well done.