It is well known that energetic protons having a ring-type, anisotropic velocity distribution can generate low-frequency electromagnetic waves, propagating nearly transverse to the geomagnetic field lines, in the ring current region of the Earth's magnetosphere by exciting mode 1 and mode 2 non-resonant instabilities and a resonant instability. In this paper, detailed investigations of the resonant and non-resonant instabilities are conducted as a function of plasma parameters such as ring speeds, electron temperatures, magnetic field strength and wave propagation directions. Our analysis is for parameters corresponding to the ring current region of the Earth's magnetosphere.