The Euler-Lagrange equations for a charged particle in a tokamak magnetic fieid, in the limit of large aspect ratio, are obtained in terms of toroidal coordinates from the exact Lagrangian, which is expressed in terms of the toroidal and poloidal magnetic fluxes. It differs fundamentally from the standard guiding-center approach, where the local magnetic-field direction defines a spatial axis, and where there is no direct link between the velocity coordinates and the time derivatives of the spatial coordinates, so that application to the particular magnetic geometry of the tokamak is often difficult. In contrast, the tokamak magnetic field is specified at the outset in the present approach. For example, cyclotron motion in the combined poloidal and toroidal fields appears as a libration in real space, superimposed on motion composed of linear nonoscillatory and averaged quadratic oscillatory terms. The primary application that is considered concerns the plasma response to high-frequency waves, using both cold plasma and kinetic treatments. A kinetic expression for cyclotron resonance is obtained that agrees with the gyrokinetic result [see, for example, C. N. Lashmore-Davies and R. 0. Dendy, Phys. Fluids B1, 1565 (1989) and references therein], which differs from the standard expression.