Convert $6$ radians into degree measure.
Convert $6$ radians into degree measure.
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.
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