The LHCb experiment at CERN has produced many intriguing results in b->sll and b->clν decays, which point to potential contributions from New Physics. This thesis describes an analysis of B0->K*0μ+μ- where the decay amplitudes are measured as functions of q2, the dimuon invariant mass squared. Measuring the angular distribution of this decay results in a plethora of observables that can be used to constrain the type of New Physics contributions. Owing to the number of parameterisations of the Standard Model and other models which can describe New Physics effects, Legendre polynomial ansatzes are used to describe the variation with q 2 in order to be as model-independent as possible. A selection strategy for B0->K*0μ+μ- is outlined, resulting in low levels of misidentified and combinatorial background. Pseudoexperiment studies are performed in order to develop the analysis strategy and further understand the symmetries of the angular distribution and the fit. Blinded results from 9 fb−1 of data collected by the LHCb detector at the LHC at CERN are shown, where the fit is performed in the region 1.25 < q2 < 8 GeV2/c4 . The fit is performed with four-parameter ansatzes for the P-wave and one-parameter ansatzes for the S-wave. Pseudoexperiment studies are performed from the data fit. The data fit quality is determined to be good, with p-value = 70%. Where the Hessian is not a good description of the uncertainties, fits to the log-likelihood profiles are performed with bifurcated parabolas to extract the uncertainties, resulting in good-quality statistical coverage.