Trigonometry: Pythagorean Identity

$$\frac{3}{2}\sin(x) = \cos^2(x)$$

If $-\frac{\pi}{2} \le x \le \frac{\pi}{2}$ , what is $\frac{\pi}{x}$?

Hint: Remember, $\sin^2(x) + \cos^2(x) = 1$.