We report an indirect search for nonstandard model physics using the flavor-changing neutral current decays B→K(*)μ(+)μ(-). We reconstruct the decays and measure their angular distributions, as a function of q(2)=M(μμ)(2)c(2), where M(μμ) is the dimuon mass, in pp¯ collisions at √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)μ(+)μ(-) and B(+)→K(*+)μ(+)μ(-). The B→K*μ(+)μ(-) forward-backward asymmetry in the most sensitive kinematic regime, 1≤q(2)<6 GeV(2)/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.