Chapter 6 - Analytic Trigonometry - Section 6.2 The Inverse Trigonometric Functions (Continued) - 6.2 Assess Your Understanding - Page 480: 40

$\dfrac{\pi}{4}$

We know that the trigonometric function $\csc^{-1} x$ has range: $[-\dfrac{\pi}{2}, 0) \cup (0, \dfrac{\pi}{2}]$. Here, $\csc^{-1} (\sqrt 2)=\dfrac{\pi}{4}$, because $\csc(\dfrac{\pi}{4})=\sqrt 2$ and $\dfrac{\pi}{4}$ lies in the range of $\csc^{-1}{x}$ .