I was working today in the equation of a pendulum: What I got is $$t = f (\theta)=k\cdot \int_0^\theta {\frac{du}{\sqrt {\cos u}}}$$ Where $k $ is a constant.
I know that this function has an inverse, but I didn't know how to find that inverse.
Can you please help me to do that?
( If it is not possible to express it as a closed form expression or as an integral, can you at least express it as an infinite serie?)