Understand the problem: We need to evaluate the expression \( \cos^{-1}(\cos(\frac{\pi}{2})) \). This involves understanding the properties of the inverse cosine function.
Recall the definition of the inverse cosine function: \( \cos^{-1}(x) \) is the angle \( \theta \) such that \( 0 \leq \theta \leq \pi \) and \( \cos(\theta) = x \).
Evaluate the inner function: Calculate \( \cos(\frac{\pi}{2}) \). Since \( \frac{\pi}{2} \) is 90 degrees, \( \cos(\frac{\pi}{2}) = 0 \).
Substitute the result into the inverse function: We now have \( \cos^{-1}(0) \).
Determine the angle: Find the angle \( \theta \) such that \( \cos(\theta) = 0 \) and \( 0 \leq \theta \leq \pi \). The angle that satisfies this condition is \( \frac{\pi}{2} \).