Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 4 - Section 4.3 - Vertical and Horizontal Translations - 4.3 Problem Set - Page 218: 60

Answer

$Amplitude = 2$ $Period = 4\pi$ $Horizontal\ shift = \pi $ (right shift $\pi$) $Vertical\ shift = 3$ (3 units shift upward) $Phase = -\frac{\pi}{2}$

Work Step by Step

If C is any real number and $B> 0$, then the graphs of $y = k + A\sin(Bx+C)$ and $y = k + A\cos (Bx+C)$ will have $Amplitude = |A|$ $Period = \frac{2\pi}{B}$ $Horizontal\ shift = –\frac{C}{B}$ $Vertical\ shift = k$ $Phase = C$ so for $y = 3 + 2\sin (\frac{1}{2}x - \frac{\pi}{2})$ $Amplitude = |2| = 2$ $Period = \frac{2\pi}{\frac{1}{2}} = 4\pi$ $Horizontal\ shift = (–\frac{-\frac{\pi}{2}}{\frac{1}{2}}) = \pi $ (right shift) $Vertical\ shift = 3$ (3 units shift upward) $Phase = -\frac{\pi}{2}$
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