Evaluate the expression.
$\cos^{-1}\left(0\right)$

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

Answer: (B)

Verified step by step guidance

1. Understand that \( \cos^{-1}(x) \) is the inverse cosine function, which gives the angle whose cosine is \( x \).
2. Recognize that the problem asks for \( \cos^{-1}(0) \), meaning we need to find the angle \( \theta \) such that \( \cos(\theta) = 0 \).
3. Recall that the cosine of an angle is 0 at specific points on the unit circle. These points are \( \frac{\pi}{2} \) and \( \frac{3\pi}{2} \).
4. Since the range of the inverse cosine function \( \cos^{-1}(x) \) is \([0, \pi]\), we need to select the angle within this range.
5. Identify that \( \frac{\pi}{2} \) is within the range \([0, \pi]\), while \( \frac{3\pi}{2} \) is not. Therefore, \( \cos^{-1}(0) = \frac{\pi}{2} \).