Question 756289

Note that csc x=1 / sin x. sin x has a range of [-1,1], so the range of csc x is (-inf,-1] U [1,inf]. 

There are many other functions that have that range, like any function that is 1/f(x) where f(x) is a function with a range of [-1,1]. Actually, and function that has a range of [-1,1] has a reciprocal that when treated as a function, has the same range as y=csc x.