Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Graphs of the Circular Functions - Section 4.4 Graphs of the Secant and Cosecant Functions - 4.4 Exercises - Page 180: 36


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 $(-\infty, -2] \cup [2, +\infty)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.