# Chapter 4 - Quiz (Sections 4.1-4.2) - Page 164: 3

$y = -\frac{1}{2}~cos~2x$ We can see the graph below. The period is $\pi$ The amplitude is $\frac{1}{2}$

#### Work Step by Step

$y = -\frac{1}{2}~cos~2x$ When $x = 0$, then $y = -\frac{1}{2}~cos~0 = -\frac{1}{2}$ When $x = \frac{\pi}{4}$, then $y = -\frac{1}{2}~cos~\frac{\pi}{2} = 0$ When $x = \frac{\pi}{2}$, then $y = -\frac{1}{2}~cos~\pi = \frac{1}{2}$ When $x = \frac{3\pi}{4}$, then $y = -\frac{1}{2}~cos~\frac{3\pi}{2} = 0$ When $x = \pi$, then $y = -\frac{1}{2}~cos~2\pi = -\frac{1}{2}$ We can see the graph below. The period is $\pi$ The amplitude is $\frac{1}{2}$

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