what is the range of ( y = csc(x) )?\n( y leq - 1 )\n( y geq 1 )\n( y leq - 1 ) or ( y geq 1 )\n( - 1 leq y…

Explanation:

Step1: Recall the definition of cosecant function

(y = \csc(x)=\frac{1}{\sin(x)})

Step2: Determine the range of (\sin(x))

The range of (y = \sin(x)) is ([- 1,1]). But (\sin(x)\neq0) (since (\csc(x)=\frac{1}{\sin(x)}) and division by zero is undefined).

Step3: Analyze the reciprocal relationship

When (-1\leqslant\sin(x)<0), then (\csc(x)=\frac{1}{\sin(x)}\leqslant - 1). When (0<\sin(x)\leqslant1), then (\csc(x)=\frac{1}{\sin(x)}\geqslant1)

Answer:

(y\leqslant - 1) or (y\geqslant1) (the third option)