My understanding of math curricula over the past few decades is that, at various times, the accepted sequence has been algebra I, algebra II/trig, then geometry, or algebra I, geometry, then algebra II/trig. Logically, this means you don't need trig or geometry to do the other. In fact, the district I work in offers the former to freshman who have already had alg I (i.e., they take alg II/trig in ninth grade), and the latter to freshman who have not (mainly to insure that everyone is taking geometry during tenth grade, when state-mandated high stakes testing occurs).
We are using the Singapore Discovering Math (not Common Core) series with our own children; it is an integrated approach that interleaves pre-algebra, algebra, geometry, and trig across a nominal three and a half years. (The last half year is just test prep for the GCSE.) I have not found sliding around between trig and geometry to be a problem.
