A geometrical method developed for a particle detector can be extended for application to the determination of the pitch angle sampling capability of the particle telescope of any orientation and for the parent satellite of any orbital orientation. A unit vector tangent to a dipole geomagnetic field line has been calculated from the dipole magnetic field equations in the geomagnetic coordinate system. Rotation matrices have been used, step-by-step, to align the geomagnetic coordinate frame with the detector coordinate frame. The detector selected in this work has its axis tilted with the local zenith direction. The component of the unit vector in the detector coordinate system is found at an observation point characterized by longitude, latitude, and the geocentric radial distance. Pitch angles are measured with respect to the guiding field direction. The pitch angle sampling factor is used in the calculation of detector response functions to particles of different pitch angles. The sampling efficiency functions are useful to make an absolute comparison of magnetospheric particle fluxes measured by particle telescopes under different solar conditions pertaining to different epochs.