This is indirectly related to issues with cyclotomic polynomials and glaois groups.(adsbygoogle = window.adsbygoogle || []).push({});

Is there some easy way to know if you are dealing with a cos or sin that is expressable in terms of roots of rationals? Like [itex]\pi/3[/itex] for example? If so, is there any straightforward way of figuring it out?

I'm asking because I'm trying to do a problem involving the galois group for the 7th roots of unity. The fact that there is a order 2 and order 3 subgroup of the galois group makes me think that Q(i) must be a fixed field and then some cube root another one for the subgroups. This would further imply that [itex]cos(4\pi/7)[/itex] is expressable as a ratioal function plus a cube root (unless I'm way off in space, which is possible).

Thanks

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# Cos/Sin as roots of rationals

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