Answer
$y = -2~cos~(x+\frac{\pi}{4})$
We can see the graph below.
The period is $2\pi$
The amplitude is $2$
Work Step by Step
$y = -2~cos~(x+\frac{\pi}{4})$
When $x = 0$, then $y = -2~cos~(\frac{\pi}{4}) = -\sqrt{2}$
When $x = \frac{\pi}{4}$, then $y = -2~cos~(\frac{\pi}{2}) = 0$
When $x = \frac{3\pi}{4}$, then $y = -2~cos~(\pi)= 2$
When $x = \frac{5\pi}{4}$, then $y = -2~cos~(\frac{3\pi}{2}) = 0$
When $x = \frac{7\pi}{4}$, then $y = -2~cos~(2\pi) = -2$
When $x = 2\pi$, then $y = -2~cos~(\frac{9\pi}{4}) = -\sqrt{2}$
We can see the graph below.
The period is $2\pi$
The amplitude is $2$
