Question

Convert $6$ radians into degree measure.

• A. $343^{\circ }38^{\prime }11^{\prime \prime }$
• B. $348^{\circ }33^{\prime }11^{\prime \prime }$
• C. $433^{\circ }38^{\prime }11^{\prime \prime }$
• D. $343^{\circ }37^{\prime }12^{\prime \prime }$

Answer 1

Answer: (A)

We know that $\pi$ radian $=180^{\circ }$.
Hence, $6$. radians $=\frac{180}{\pi }\times 6$ degree $=\frac{1080\times 7}{22}$ degree
$=343\frac{7}{11}$ degree $=343^{\circ }+\frac{7\times 60}{11}$ minute $[$as $1^{\circ }=60^{\prime }]$
$=343^{\circ }+38^{\prime }+\frac{2}{11}$ minute $[$as $1^{\circ }=60^{\prime \prime }]$
$=343^{\circ }+38^{\prime }+10.9^{\prime \prime }=343^{\circ }38^{\prime }11^{\prime \prime }$ approximately.
Hence, $6$ radians $=343^{\circ }38^{\prime }11^{\prime \prime }$ approximately.