Question

Find \( \tan^{-1} (-\sqrt{3}) \).

• A. \( \frac{\pi}{6} \)
• B. \( \frac{\pi}{3} \)
• C. \( \frac{2\pi}{3} \)
• D. \( -\frac{\pi}{3} \)

Hint:

The inverse tangent of a negative value is the negative of the corresponding positive angle.

Answer 1

The Correct Option is D

We are asked to find: \[ \tan^{-1} (-\sqrt{3}) \] We know that: \[ \tan \frac{\pi}{3} = \sqrt{3} \] Since the argument is negative, we are looking for the angle in the fourth quadrant. The value of \( \tan^{-1} (-\sqrt{3}) \) is: \[ -\frac{\pi}{3} \] Thus, the correct answer is \( -\frac{\pi}{3} \).