Let S be the set of real numbers r s.t. $\displaystyle \cos (r) \in Q\sqrt 2$.

$\displaystyle Q\sqrt 2 $ be the set of real numbers of the form $\displaystyle a+b\sqrt 2 $, where a,b is rational.

Find the cardinality of S.

I know 0,2pi,4pi.. etc are in S, so S is infinite

and $\displaystyle Q\sqrt 2 $ is countably infinite (dont know if it matters)

then im not sure how to go on...any hints would be appreciated.

Thanks in advance