Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 175: 30

Answer

Domain: $(-\infty, +\infty)$ Range: $(-\infty, -2] \cup [2, +\infty)$

Work Step by Step

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 $(-\infty, -2] \cup [2, +\infty)$.
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