Question

Find the principal value $ta{n}^{-1}(-1)$

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

Answer 1

Answer: (D)

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