Convert 6 radian into degree measure. - Vidyadip

Question

Convert 6 radian into degree measure.

✓

Answer

We know, degree measure = $\frac { 180 } { \pi }$ $\times$ radian measure
$\therefore$ Required degree measure
= $\frac { 180 } { \frac { 22 } { 7 } } \times 6$ [$\because \pi = \frac { 22 } { 7 }$]
= $\frac { 1080 \times 7 } { 22 }$ degree
$= 343$ $\frac { 7 } { 11 }$degree
$= 343^o +$ $\frac { 7 } { 11 }$ $\times$ $60\ min$ [$\because 1^o = 60'$]
$= 343^o + 38 $$\frac { 2 } { 11 }$ min
$= 343^o + 38' +$ $\frac { 2 } { 11 }$ min
$= 343^o +38' +$ $\frac { 2 } { 11 }$ $\times$ 60"
$= 343^o + 38' + 10.9"$
$=343^{\circ} 38^{\prime} 11^{\prime \prime} \text { (approx) }$
$\text { Hence, } 6 \mathrm{rad}=343^{\circ} 38^{\prime} 11^{\prime \prime} \text { (approx) }$

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