The domain  of f(x)  =sin−1⁡[x] (where [ ] represents the greatest integer function).

f(x)=sin−1⁡[x] is defined if     −1≤[x]≤1 or     [x]=−1,0,1 or      x∈[−1,2) So, range is sin−1⁡(−1),sin−1⁡0,sin−1⁡1≡{−π2,0,π2}