The value of $\arctan(1)$, or the inverse tangent of $1$, represents the angle whose tangent is $1$. In radians:

$\arctan(1) = \frac{\pi}{4}$

In degrees:

$\arctan(1) = 45^\circ$

This is because $\tan\left(\frac{\pi}{4}\right) = 1$.

Would you like further details or have any questions? Here are some related queries for exploration:

1. What is $\arctan(-1)$?
2. How does $\arctan(x)$ relate to $\tan^{-1}(x)$?
3. What are the properties of the $\arctan(x)$ function?
4. How do you compute $\arctan(x)$ for values other than 1?
5. How is the arctangent function used in physics or engineering?

Tip: Always remember that the range of the $\arctan(x)$ function is $-\frac{\pi}{2}$ to $\frac{\pi}{2}$, which helps to determine the angle's quadrant.