Simple pendulum approximation

The function [Fθ/sin (Fθ)]1/2 with F equal to approximately (3)1/2/2 is a close fit to the relative period of a simple pendulum as a function of amplitude. The fit is better than 5% up to 160°, and for 0°–100° the fit is better than ±0.001. Moreover, it can be derived without calculus.