In the course of working on some correlation problem, I happened to notice that in the vicinity of $0$, $\cos^n x$ is a pretty darned good approximation to $\exp\left(\frac{-nx^2}{2}\right)$. In other words, one can approximate a normal distribution with a high power of cosine.
This turned out to be useful to me in the opposite direction, because I had a PDF that was a high power of cosine, and I could use the normal approximation. But it occurred to me that this is simple enough to see (I arrived at it using the first two terms of the Taylor series for cosine, but there are other ways, I imagine) that it must have been noticed before, but not so old that it would be prehistoric (mathematically speaking), and without a known discoverer.
So, does anyone know who first noticed this? Or is this lost to the sands of time because it is so easily found?