Chapter 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 480: 38

$\dfrac{\pi}{4}$

We know that the trigonometric function $\cot^{-1} x$ has range: $(0, \pi)$. Here, $\cot^{-1} (1)=\dfrac{\pi}{4}$, because $\cot(\dfrac{\pi}{4})=\dfrac{1}{1}=1$ and $\dfrac{\pi}{4}$ lies in the range of $\cot^{-1}{x}$ .