Evaluate the expression.
$\cos^{-1}\left(-1\right)$

• A. $0$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{3\pi }{2}$

Answer: (B)

Verified step by step guidance

1. Understand the problem: We need to evaluate the expression \( \cos^{-1}(-1) \). This involves finding the angle whose cosine is \(-1\).
2. Recall the range of the \( \cos^{-1} \) function: The inverse cosine function, \( \cos^{-1}(x) \), returns values in the range \([0, \pi]\).
3. Identify the angle: The cosine of \( \pi \) is \(-1\), so \( \cos^{-1}(-1) = \pi \).
4. Verify the solution: Check that \( \pi \) is within the range \([0, \pi]\), which confirms that \( \pi \) is a valid output for \( \cos^{-1}(-1) \).
5. Conclude: The value of \( \cos^{-1}(-1) \) is \( \pi \), which is consistent with the properties of the inverse cosine function.