To evaluate the function \( f(x) = -\cos(x) \) at \( x = \frac{\pi}{2} \), we first need to find \( \cos\left(\frac{\pi}{2}\right) \).
We know that: \[ \cos\left(\frac{\pi}{2}\right) = 0 \]
Now, substituting this value into the function: \[ f\left(\frac{\pi}{2}\right) = -\cos\left(\frac{\pi}{2}\right) = -0 = 0 \]
Thus, the value of the function \( f\left(\frac{\pi}{2}\right) \) is: \[ \boxed{0} \]