## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\dfrac{\pi}{4}$
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 $\cot^{-1}{x}$ .