what is the range of y = csc(x)?\no y≤ - 1\no y≥1\no y≤ - 1 or y≥1\no - 1≤y≤1

Explanation:

Step1: Recall the definition of cosecant

The cosecant function is defined as $\csc(x)=\frac{1}{\sin(x)}$.

Step2: Analyze the range of sine

The range of the sine function is $- 1\leqslant\sin(x)\leqslant1$.

Step3: Analyze the reciprocal

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

Answer:

$y\leqslant - 1$ or $y\geqslant1$