Abstract Algebra Problems

Question Description

I’m working on a algebra multi-part question and need the explanation and answer to help me learn.

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Notes:
For (b) Find at least three different subfields F with [F : Q] = 2 (you do not need to find all subfields). For
(c) Find at least two different subfields with [F : Q] = 4 (you do not need to find all subfields).
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Hints: Using the identities cos(?+?) = cos ? cos ??sin ? sin ?, sin 2? = 2 sin ? cos ? and cos 2? = 2 cos^2
? ? 1 repeatedly, it is possible to express cos 5? as a polynomial in cos ?. See also the part about
trisecting an angle.
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