Question

Find the principal value $tan^{-1} \, (-1)$

• A. $\frac{2\pi}{3}$
• B. $\frac{\pi}{10}$
• C. $\frac{3\pi}{4}$
• D. $-\frac{\pi}{4}$

Answer 1

Answer: (D)

Let $tan^{-1} \left(-1\right) = \theta$
$\Rightarrow tan\,\theta = -1$
$= -tan \frac{\pi}{4}$
$= tan \left(-\frac{\pi }{4}\right)$
$\Rightarrow \theta = -\frac{\pi }{4} \in \left(\frac{-\pi }{2}, \frac{\pi }{2}\right)$
$\therefore $ Principal value of $tan^{-1} \left(-1\right)$ is $\frac{-\pi }{4}$