Find the principal value of ^ -1 (-3). - Vidyadip

Question

Find the principal value of $\tan ^{-1}(-\sqrt{3})$.

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Answer

We know that for any $x \in R, \tan^{-1}x$ represents an angle in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ whose tangent is $x$.
Therefore,
$\tan^{-1}(-\sqrt{3})$ $=\left(\text { An angle } \theta \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \text { such that } \tan \theta=-\sqrt{3}\right)$
$=-\frac{\pi}{3}$

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