Find sin⁻¹(sin 9) and cos⁻¹(cos 9), with 9 in radians…

Step 1. Reduce. $9 - 2\pi = 2.7168$, which lies between $\dfrac{\pi}{2} = 1.5708$ and $\pi = 3.1416$.

Step 2. The cosine. $2.7168$ is in $[0, \pi]$, so $\cos^{-1}(\cos 9) = 2.7168$.

Step 3. The sine. $2.7168$ is outside $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$. The result is $\pi - 2.7168 = 0.4248$.

Step 4. The sum. $0.4248 + 2.7168 = 3.1416$. In symbols the sum is $(\pi - u) + u = \pi$ for $u = 9 - 2\pi$.