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