Answer
$y=1-\ cos(\frac{4\pi}{3}x)$
Work Step by Step
Step 1. Shift the curve 1 unit down, we can see the new curve will be even and passes $(0,-1)$, thus we can write a general form $y=1-A\ cos(kx)$
Step 2. We can identify the amplitude $A=1$.
Step 3. We can identify the period $p=\frac{3}{2}$, thus $\frac{2\pi}{k}=\frac{3}{2}$ and $k=\frac{4\pi}{3}$
Step 4. The equation is $y=1-\ cos(\frac{4\pi}{3}x)$
