We know that $\pi$ radian $=180^{\circ}$

Hence $6 \text { radians }=\frac{180}{\pi} \times 6 \text { degree }=\frac{1080 \times 7}{22} \text { degree }$

${ = 343\frac{7}{{11}}{\text{ degree }} = {{343}^\circ } + \frac{{7 \times 60}}{{11}}{\text{ minute }}\left[ {{\text{ as }}{1^\circ } = {{60}^\prime }} \right]}$

${ = {{343}^\circ } + {{38}^\prime } + \frac{2}{{11}}{\text{ minute }}}$     ${[{\text{as }}{{\text{1}}^\prime }{\text{ = 6}}{{\text{0}}^{\prime \prime }}]}$

${ = {{343}^\circ } + {{38}^\prime } + {{10.9}^{\prime \prime }}}$      $=343^{\circ} 38^{\prime} 11^{\prime \prime}$ approximately

Hence $6$ radians $=343^{\circ} 38^{\prime} 11^{\prime \prime}$ approximately.