Question

Evaluate \[\tan^{-1}(-\sqrt{3})\].

Options

• \[\frac{\pi}{3}\]

• \[-\frac{\pi}{3}\]

• \[-\frac{2\pi}{3}\]

• \[\frac{2\pi}{3}\]

Answer 1

The principal value range of \[\tan^{-1}x\] is \[\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\]. Since \[\tan\left(-\frac{\pi}{3}\right)=-\sqrt{3}\], the required value is \[-\frac{\pi}{3}\].