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 the problem: We need to evaluate the inverse cosine function, \( \cos^{-1}(0) \). This function asks for the angle whose cosine is 0.
2. Recall the range of the \( \cos^{-1} \) function: The inverse cosine function returns values in the interval \([0, \pi]\). This means we are looking for an angle between 0 and \( \pi \) radians.
3. Identify the angle: The cosine of \( \frac{\pi}{2} \) is 0. Therefore, \( \cos^{-1}(0) = \frac{\pi}{2} \).
4. Verify the solution: Check that \( \cos(\frac{\pi}{2}) = 0 \) to ensure the angle is correct.
5. Conclude: The value of \( \cos^{-1}(0) \) is \( \frac{\pi}{2} \), which is within the range of the inverse cosine function.