1. The problem involves understanding the inverse tangent function, often written as $\tan^{-1}(x)$ or $\arctan(x)$, which gives the angle whose tangent is $x$. 2. To find $\arctan(x)$, we look for an angle $\theta$ such that $\tan(\theta) = x$. 3. The range of $\arctan(x)$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, meaning the output angle is always between $-90^\circ$ and $90^\circ$. 4. For example, if $x=1$, then $\arctan(1) = \frac{\pi}{4}$ because $\tan\left(\frac{\pi}{4}\right) = 1$. 5. To solve equations involving $\arctan$, isolate the inverse tangent and then apply the tangent function to both sides to remove the inverse, remembering to consider the domain and range. 6. Example: Solve $\arctan(x) = \frac{\pi}{6}$. 7. Apply tangent to both sides: $x = \tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}}$. 8. Thus, $x = \frac{1}{\sqrt{3}}$ is the solution. This explanation covers the concept and basic use of the inverse tangent function.