The principal value of $\tan^{-1}(1)$ is

A$\tfrac{\pi}{3}$

B$\tfrac{\pi}{4}$

C$\tfrac{\pi}{2}$

D$\tfrac{\pi}{6}$

Answer & Solution

Correct answer: B. $\tfrac{\pi}{4}$

$\tan^{-1}$ returns values in $\left(-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right)$. We need $\tan\theta = 1$ with $\theta$ in that range, which gives $\theta = \tfrac{\pi}{4}$.

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