Question 756289: Which function has the same range as y=csc x
Answer by algebraic penguin(13)   (Show Source):
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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.
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