Find sin⁻¹(sin 6), cos⁻¹(cos 8) and tan⁻¹(tan 3). All angles are in radians.

Step 1. The sine. $6 - 2\pi = -0.2832$, which lies in $\left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right]$. So $\sin^{-1}(\sin 6) = -0.2832$.

Step 2. The cosine. $8 - 2\pi = 1.7168$, which lies in $[0, \pi]$. So $\cos^{-1}(\cos 8) = 1.7168$.

Step 3. The tangent. $3$ lies between $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2}$, so $\tan^{-1}(\tan 3) = 3 - \pi = -0.1416$.