# Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 264: 20

$-\displaystyle \frac{\pi}{4}$

#### Work Step by Step

lnverse Tangent Function: $y=\tan^{-1}x$ or $y=$ arctan $x \quad$means that $x=\tan y$, for $-\displaystyle \frac{\pi}{2} < y < \frac{\pi}{2}$. ---------- In the interval$\quad -\displaystyle \frac{\pi}{2} < y < \frac{\pi}{2}$ , we find $y=-\displaystyle \frac{\pi}{4}$ to be such that $\displaystyle \tan(-\frac{\pi}{4})=-1$. So $y=\displaystyle \tan^{-1}(-1)=-\frac{\pi}{4}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.