Evaluate \( \cos^{-1}(\cos 3) \)
Step-by-Step Solution
We need to evaluate:
\[ \cos^{-1}(\cos 3) \]
Step 1: Principal value range
The principal value range of \( \cos^{-1}x \) is:
\[ [0, \pi] \]
Step 2: Check the angle
Since \( 3 \in (0, \pi) \), it already lies in the principal range.
Step 3: Apply inverse cosine
\[ \cos^{-1}(\cos 3) = 3 \]
Final Answer
\[ \boxed{3} \]