Show that the two given sets have equal cardinality by describing a bijection from one to the other

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Show that the two given sets have equal cardinality by describing a bijection from one to the other. Describe your bijection with a formula (i.e. not as a table)

My two sets are: (The set of all integers) and set S = {x ∈ (the set of all real numbers) : sin(x) = 1}

I know I need to make sure it is both injective and surjective, and find some f -> S defined by (some function, I suspect the answer is f(n) = (2*pi)(n) - (3pi/2) because the set of all real numbers where sin(x) =1, are all 2pi multiples of pi/2. i.e., pi/2, (2pi)(pi/2), (4pi)(pi/2), etc.)

Past that, I'm unsure on how I can prove these sets are equal in cardinality with a bijection. Thank you for any help!