Finding the minimal polynomials of trigonometric expressions quickly If if an exam I had to calculate the minimal polynomials of, say, $\sin(\frac{2 \pi}{5})$ or $\cos(\frac{2 \pi}{19})$, what would be the quickest way to do it? I can use the identity $e^{ \frac{2 i \pi}{n}} = \cos(\frac{2 \pi}{n}) + i\sin(\frac{ 2 \pi}{n})$ and raise to the power $n$, but this gets nasty in the $n = 19$ case...
Thanks

William E. Heierman has a nice, simple, generic and quick method here. It would have no problem with $n=19$ (the original example is for $n=15$).
Since it is a recurrent question, and nice application of cyclotomic polynomials, I chose to expose it in French Wikipedia.
