Trigonometry (11th Edition) Clone

Domain: $(-\infty, +\infty)$ Range: $(-\infty, -2] \cup [2, +\infty)$
RECALL: The cosecant function $y=\csc{x}$ has: (1) $(-\infty, +\infty)$ (the set of real numbers) as its domain; and (2) $(-\infty, -1] \cup [1, +\infty)$ as its range. The value of the function is never in the interval $(-1, 1)$. Thus, the domain of the given function is also the set of real numbers. The given function has $2$ as a multiplier outside the cosecant function. The value of the given function is will never be between $-2$ and $2$ so its range is $(-\infty, -2] \cup [2, +\infty)$.