We have measured the cross section for quasielastic 1p-shell proton knockout in the 16O(e,e(')p) reaction at omega = 0.439 GeV and Q2 = 0.8 (GeV/c)(2) for missing momentum P(miss)</=355 MeV/c. We have extracted the response functions R(L+TT), R(T), R(LT), and the left-right asymmetry, A(LT), for the 1p(1/2) and the 1p(3/2) states. The data are well described by relativistic distorted wave impulse approximation calculations. At large P(miss), the structure observed in A(LT) indicates the existence of dynamical relativistic effects.