>I know how to write the set {..., -2pi, -pi, 0, pi, 2pi,...} = { sine x = 0 | x belongs to Z } and {..., -3pi/2, pi/2, 5pi/2,...} = { sine x = 1 | x belongs to Z } separately.

these are both wrong. first of all, you should not have an equation on the left side of the | when writing a set, that doesn't really make much sense (unless you want the elements of your set to be "true" or "false", instead of numbers). also, the other mistake is that you wrote x is in Z, but you probably meant x is in R. so the first set should be {x | x in R and sin(x) = 0} and the second, {x | x in R and sin(x) = 1}.

also, I don't see why you are writing the sets using sine at all. why not just write  {..., -2pi, -pi, 0, pi, 2pi,...} as {n pi | n in Z}? then the set you want is just {n pi/2 | n in Z}.

alternatively if you do want to write it in terms of sine, you could just write it as the set of x such that sin(x) = 0 or sin(x) = 1.

>{..., -3/2, -3/4, 0, 3/4, 3/2, 9/4, 3, 15/4, 9/2,...}

and this is just multiples of 3/4. {3n/4 | n in Z}.

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