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Let $$g(x)=\left[\frac{1}{\operatorname{cosec}x}\right]$$, Then the range of $$g(x)$$ is ($$\mathbb{Z}$$ is the set of integers.)
Since $$\frac{1}{\operatorname{cosec}x}=\sin x$$, we have $$-1\le\sin x\le1$$. The greatest-integer value of a number in this interval can only be $$-1$$, $$0$$, or $$1$$. All three values occur, so the range is $$\{-1,0,1\}$$.
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