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 that \( \tan^{-1}(x) \) is the inverse tangent function, also known as arctan, which gives the angle whose tangent is \( x \).
2. Recognize that \( \tan^{-1}(0) \) asks for the angle whose tangent is 0.
3. Recall that the tangent of an angle is 0 at specific points on the unit circle. Specifically, \( \tan(0) = 0 \).
4. Therefore, \( \tan^{-1}(0) = 0 \) because the angle whose tangent is 0 is 0 radians.
5. Conclude that the value of the expression \( \tan^{-1}(0) \) is 0, which corresponds to the angle 0 radians.