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 q2=M2μμc2, where Mμμ 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(2)T and the time-reversal-odd charge-and-parity asymmetry Aim are measured for the first time, together with the K∗ longitudinal polarization fraction FL and the muon forward-backward asymmetry AFB for the decays B0→K*0μ+μ− and B+→K*+μ+μ−. The B→K∗μ+μ− forward-backward asymmetry in the most sensitive kinematic regime, 1≤q2<6  GeV2/c2, is measured to be AFB=0.29+0.20−0.23(stat)±0.07(syst), the most precise result to date. No deviations from the standard model predictions are observed.