Catalyzes the cyclization of farnesyl diphosphate to alpha-copaene and (+)-delta cadinene. (2E,6E)-farnesyl diphosphate = (1S,8aR)-delta-cadinene + diphosphate (2E,6E)-farnesyl diphosphate = alpha-copaene + diphosphate Binds 3 Mg(2+) ions per subunit. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.