1. The problem asks to find the value of the expression $\cos^{-1} 0$. 2. The function $\cos^{-1} x$ (also called arccosine) gives the angle $\theta$ in radians whose cosine is $x$, with the principal value range $0 \leq \theta \leq \pi$. 3. We need to find $\theta$ such that $\cos \theta = 0$. 4. From the unit circle, $\cos \theta = 0$ at $\theta = \frac{\pi}{2}$ within the principal range. 5. Therefore, the value of $\cos^{-1} 0$ is: $$\cos^{-1} 0 = \frac{\pi}{2}$$ This means the angle whose cosine is zero is $\frac{\pi}{2}$ radians (or 90 degrees).