What is the range of the function $y = csc x$ $y = csc x$ ?

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Answer 1 · 2014-09-27T01:54:56

The range of $csc x$ $cscx$ is $(- \infty, - 1] \cup [1, \infty)$ $(-infty,-1]cup[1,infty)$ .

Let us look at some details.

We know

$| sin x | \leq 1$ $|sinx| le 1$

by taking the reciprocal,

$\Rightarrow | csc x | = \frac{1}{| sin x |} \geq 1$ $Rightarrow |cscx|=1/|sinx| ge 1$

(Note that we need to switch the direction of inequality.)

Hence, its range is $(- \infty, - 1] \cup [1, \infty)$ $(-infty,-1]cup[1,infty)$ .

What is the range of the function y=cscxy = csc x?