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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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