Chapter 4 - Graphs of the Circular Functions - Summary Exercises on Graphing Circular Functions - Page 181: 3

$y = -2+\frac{1}{2}~cos~\frac{\pi}{4}x$ We can see the graph below.

$y = -2+\frac{1}{2}~cos~\frac{\pi}{4}x$ When $x = 0$, then $y = -2+\frac{1}{2}~cos~0 = -1.5$ When $x = 2$, then $y = -2+\frac{1}{2}~cos~(\frac{\pi}{2}) = -2$ When $x = 4$, then $y = -2+\frac{1}{2}~cos~(\pi)= -2.5$ When $x = 6$, then $y = -2+\frac{1}{2}~cos~(\frac{3\pi}{2}) = -2$ When $x = 8$, then $y = -2+\frac{1}{2}~cos~(2\pi) = -1.5$ We can see the graph below.