We present a detailed analysis of observations of the high-mass X-ray binary Cen X-3, spanning two consecutive binary orbits performed with the RXTE satellite in early March 1997. During this time Cen X-3 had a luminosity of L 2Y10 keV $ (4Y5) ; 10 37 ergs s À1 and a pulse period of 4.814 s. The PCA and HEXTE light curves both show a clear reduction in count rate after midorbit for both binary revolutions. We therefore analyze two broadband spectra for each orbit, before and after midorbit. Consistent with earlier observations, these four joint PCA and HEXTE spectra can be well described using a phenomenological pulsar continuum model, including an iron emission line and a cyclotron resonance-scattering feature. While no strong spectral variations were detected, the second half of orbit 2 shows a tendency toward being softer and more strongly absorbed. In order to follow the orbital phase-dependent evolution of the spectrum in greater detail, we model spectra for shorter exposures, confirming that most spectral parameters show either a gradual or sudden change for the second half of the second orbit. A comparison with a simple wind model indicates the existence of an accretion wake in this system. We also present and discuss highresolution pulse profiles for several different energy bands, as well as their hardness ratios. PCA and HEXTE spectra were created for 24 phase bins and fitted using the same model as in the phase-averaged case. Systematic pulse phasedependent variations of several continuum and cyclotron line parameters were detected, most notably a significant increase of the cyclotron line energy during the early rise of the main peak, followed by a gradual decrease. We show that applying a simple dipole model for the magnetic field is not sufficient to describe our data.