An analytical approximation of a pendulum trajectory is developed for large initial angles. Instead of using a perturbation method, a succession of just two polynomials is used in order to get simple integrals. By obtaining the approximated period, the result is compared with the Kidd-Frogg and Hite formulas for the period which are very close to the exact solution for the considered angle.
Salinas-Hernández, E., Ares De Parga, G., Domínguez-Hernández, S., & Muñoz-Vega, R. (2014). An analytical approximation of a pendulum trajectory. European Journal of Physics. https://doi.org/10.1088/0143-0807/35/4/045027