A frothy function in laymans' terms is a function that maps a rational number "x" onto an irrational number and vice versa, with either a finite number of exceptions across the range of values of x or a finite number of exceptions over a period of the function.

It's been proven that the cosine function satisfies the first condition to be a frothy function, that is, it maps a rational number θ given in degrees onto an irrational number except for a few points.

The converse has not been proven so it not known whether a cosine function is a true frothy function. But if it were, that would be a very interesting thing, because the cosine is at the heart of much mathematics.