1. **State the problem:** Explain the meaning of the function $\arctan$. 2. **Definition:** The function $\arctan$ is the inverse of the tangent function $\tan$. 3. **Explanation:** For an angle $\theta$, $\tan(\theta)$ gives the ratio of the opposite side to the adjacent side in a right triangle. 4. **Inverse function:** $\arctan$ takes a ratio (a real number) and returns the angle $\theta$ whose tangent is that number. 5. **Range:** The output of $\arctan$ is an angle in radians, typically between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$. 6. **Usage:** If $y = \arctan(x)$, then $\tan(y) = x$ and $y$ is the angle whose tangent is $x$. 7. **Summary:** $\arctan$ helps find an angle when you know the tangent value, useful in trigonometry and geometry.