Evaluate the expression.
$\(\tan\)^{-1}0$

• A. $0$
• B. $\(\frac{\pi}{2}\)$
• C. $\(\pi\)$
• D. $-\(\frac{\pi}{2}\)$

Answer: (A)

Verified step by step guidance

1. Understand the problem: We need to evaluate the expression \( \tan^{-1}(0) \). This involves finding the angle whose tangent is 0.
2. Recall the definition of the inverse tangent function: \( \tan^{-1}(x) \) gives the angle \( \theta \) such that \( \tan(\theta) = x \).
3. Consider the range of \( \tan^{-1}(x) \): The principal value of \( \tan^{-1}(x) \) is typically between \( -\frac{\pi}{2} \) and \( \frac{\pi}{2} \).
4. Identify the angle whose tangent is 0: The tangent of 0 is 0, so \( \tan^{-1}(0) = 0 \).
5. Conclude the evaluation: Since \( \tan^{-1}(0) = 0 \), the expression evaluates to 0.