To evaluate the function \( f(x) = -\cos(x) \) at \( x = \frac{\pi}{2} \), we first find the cosine of \( \frac{\pi}{2} \):
\[ \cos\left(\frac{\pi}{2}\right) = 0 \]
Now we substitute 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 at \( x = \frac{\pi}{2} \) is
\[ \boxed{0} \]