Abstract: We report an indirect search for nonstandard model physics using the flavor-changing neutral current decays B -> K-(*)mu(+)mu(-). We reconstruct the decays and measure their angular distributions, as a function of q(2) = M(mu mu)(2)c(2), where M-mu μis the dimuon mass, in p (P) over bar collisions at root s = 1.96 Tev using a data sample corresponding to an integrated luminosity of 6.8 fb(-1). The transverse polarization asymmetry A(T)((2)) and the time-reversal-odd charge-and-parity asymmetry A(im) are measured for the first time, together with the K* longitudinal polarization fraction F-L and the muon forward-backward asymmetry A(FB) for the decays B-0 -> K*(0)mu(+)mu(-) and B -> K*(+)mu(+)mu(-). The B -> K*mu(+)mu(-) forward-backward asymmetry in the most sensitive kinematic regime, 1 <= q(2) < 6 GeV2/c(2), is measured to be A(FB) 0.29(-0.23)(+0.20) (stat) +/- 0.07 (syst), the most precise result to date. No deviations from the standard model predictions are observed.