It means that y = cosec x assumes all real values except –1 < y < 1 and is
not defined for integral multiple of π If we restrict the domain of cosec function to
,
2 2
π π

−


 – {0}, then it is one to one and onto with its range as the set R – (– 1, 1) Actually,
cosec function restricted to any of the intervals 
3 ,
{
}
2
2
− π −π
 − −π




, 
2,
2
−π π




  – {0},
,3
{ }
2
2
π
π

 − π




 etc , is bijective and its range is the set of all real numbers R – (–1, 1)