Find the principal values of sec⁻¹(-√2), cosec⁻¹(-2/√3) and cot⁻¹(-1/√3), in radians.

Step 1. The secant. $\sec^{-1}\left(-\sqrt{2}\right) = \cos^{-1}\left(-\dfrac{1}{\sqrt{2}}\right) = \pi - \dfrac{\pi}{4} = \dfrac{3\pi}{4} = 2.3562$.

Step 2. The cosecant. $\operatorname{cosec}^{-1}\left(-\dfrac{2}{\sqrt{3}}\right) = \sin^{-1}\left(-\dfrac{\sqrt{3}}{2}\right) = -\dfrac{\pi}{3} = -1.0472$.

Step 3. The cotangent. $\cot\dfrac{\pi}{3} = \dfrac{1}{\sqrt{3}}$. The angle in $(0, \pi)$ with the cotangent $-\dfrac{1}{\sqrt{3}}$ is $\pi - \dfrac{\pi}{3} = \dfrac{2\pi}{3} = 2.0944$.