Trigonometry (11th Edition) Clone

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

Chapter 4 - Quiz (Sections 4.1-4.2) - Page 164: 5

Answer

$y = -2~cos~(x+\frac{\pi}{4})$ We can see the graph below. The period is $2\pi$ The amplitude is $2$

Work Step by Step

$y = -2~cos~(x+\frac{\pi}{4})$ When $x = 0$, then $y = -2~cos~(\frac{\pi}{4}) = -\sqrt{2}$ When $x = \frac{\pi}{4}$, then $y = -2~cos~(\frac{\pi}{2}) = 0$ When $x = \frac{3\pi}{4}$, then $y = -2~cos~(\pi)= 2$ When $x = \frac{5\pi}{4}$, then $y = -2~cos~(\frac{3\pi}{2}) = 0$ When $x = \frac{7\pi}{4}$, then $y = -2~cos~(2\pi) = -2$ When $x = 2\pi$, then $y = -2~cos~(\frac{9\pi}{4}) = -\sqrt{2}$ We can see the graph below. The period is $2\pi$ The amplitude is $2$
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