Trigonometry (11th Edition) Clone

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

Chapter 4 - Test - Page 194: 11

Answer

$y = -csc~2x$ The asymptotes have the form $x = \frac{\pi}{2}n$, for any integer $n$. The period is $\pi$. We can see the graph below.

Work Step by Step

$y = -csc~2x$ When $x = -\frac{\pi}{2}$, then $y = -csc~(-\pi)~~$ (which is undefined) When $x = -\frac{\pi}{4}$, then $y = -csc~(-\frac{\pi}{2}) = 1$ When $x = 0$, then $y = -csc~0$ (which is undefined) When $x = \frac{\pi}{4}$, then $y = -csc~\frac{\pi}{2} = -1$ When $x = \frac{\pi}{2}$, then $y = -csc~\pi~~$ (which is undefined) The asymptotes have the form $x = \frac{\pi}{2}n$, for any integer $n$. The period is $\pi$. We can see the graph below.
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