Answer
$y = -\frac{1}{2}~cos~2x$
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 $\frac{1}{2}$
