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 that \( \cos^{-1}(x) \) represents the inverse cosine function, which gives the angle whose cosine is \( x \).
2. Recall that the range of the inverse cosine function \( \cos^{-1}(x) \) is \([0, \pi] \). This means the output will be an angle in radians between 0 and \( \pi \).
3. Identify that the expression \( \cos^{-1}(-1) \) asks for the angle whose cosine is \(-1\).
4. Recall that the cosine of \( \pi \) is \(-1\). Therefore, \( \cos^{-1}(-1) = \pi \).
5. Conclude that the angle corresponding to \( \cos^{-1}(-1) \) is \( \pi \), which is within the range of the inverse cosine function.