Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.2 Translate and Reflect Trigonometric Graphs - 14.2 Exercises - Skill Practice - Page 920: 42


$$y=cos(2\pi x+3)-4$$

Work Step by Step

In the last section, the given functions were sine and cosine functions in the form $y=asin(bx)$ and $y=acos(bx)$. Note, the only difference between sine and cosine functions is that, when not shifted, cosine functions are at their maximum amplitude at $x=0$, while sine functions are at $0$ at this point. Note, $\mid a\mid $ is the amplitude of the functions, and $\frac{2\pi}{b}$ is the period of these functions. All of this is still true. However, now the functions also can be shifted by $h$ units to the right and $k$ units up, as noted on page 915. Recall, it is necessary to pay attention to the sign of $h$ and $k$. (Do not forget that there is a negative in front of $h$!) Thus, we see that the equation becomes: $$y=cos(2\pi x+3)-4$$
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