3.96: Cosine curve through two points

The curve $y=a\,\mathrm{cos}\,bx+c$, where $a$, $b$ and $c$ are integers, passes through the points $\bigl(-\dfrac{\pi}{2},-2\bigr)$ and $(0,3)$. The curve has a period of $\dfrac{2\pi}{3}$.