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 179: 15

Answer

$y = csc~(x-\frac{\pi}{4})$ We can see the graph below.
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Work Step by Step

$y = csc~(x-\frac{\pi}{4})$ When $x = -\frac{3\pi}{4}$, then $y = csc~(-\pi)$ (which is undefined) When $x = -\frac{\pi}{4}$, then $y = csc~(-\frac{\pi}{2}) = -1$ When $x = \frac{\pi}{4}$, then $y = csc~0$ (which is undefined) When $x = \frac{3\pi}{4}$, then $y = csc~(\frac{\pi}{2}) = 1$ When $x = \frac{5\pi}{4}$, then $y = csc~2\pi$ (which is undefined) We can see the graph below.
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