We obtain analytical approximations for period-1 rotations of both vertically and horizontally excited pendulum using Galerkin projections with elliptic functions (GP), elliptic averaging (EA), method of multiple scales (MMS) and harmonic balance (HB). The application of GP and EA has been extended to parametrically excited pendulum for the first time in this paper, while the results from MMS and HB have been adapted from the existing literature. We compare these approximations with the numerical solution to ascertain their accuracy and identify the correct approximate solution to be used for determining other properties like stability of the solution. This comparison has been made for two different forcing frequencies: one closer to the natural frequency of the pendulum while the other at a higher frequency. We find that the appearance of the period-1 rotation at smaller amplitudes of forcing as a saddle-node bifurcation is best captured by GP and EA, but the approximation for the initial angular displacement and velocity as well as the root- mean-square error over the entire time period using GP and EA deteriorates at larger forcing amplitudes. In the large amplitude regime, HB with one-term approximation gives the best result for lower forcing frequency, while MMS results in the best approximation for the higher frequency. Inclusion of more terms in the harmonic balance approximation leads to an increased accuracy in the entire frequency and amplitude range. This observation holds for both vertical and horizontal excitation. We have also used these approximations to ascertain the stability of period-1 rotation and find that the HB approximation results in the most consistent prediction of stable parameter regimes. Hence, a multi-term HB analysis, which is the simplest and straight forward technique among the methods studied in this paper, leads to the best approximation for period-1 rotation of parametric pendula.