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

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Answer 1 · 2014-09-27T01:54:56

The range of #cscx# is #(-infty,-1]cup[1,infty)#.

Let us look at some details.

We know

#|sinx| le 1#

by taking the reciprocal,

#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)#.