Question

Convert $6$ radians into degree measure.

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

Answer 1

Answer: (A)

$343^{\circ}38'\,11''$

Answer 2

We know that $\pi$ radian $= 180^{\circ}$. Hence, $6$. radians $=\frac{180}{\pi}\times 6$ degree $=\frac{1080 \times7}{22}$ degree $=343 \frac{7}{11}$ degree $=343^{\circ}+\frac{7 \times 60}{11}$ minute $[$as $1^{\circ} = 60']$ $=343^{\circ}+38'+\frac{2}{11}$ minute $[$as $1^{\circ} = 60'']$ $= 343^{\circ} + 38' + 10.9'' = 343^{\circ}38' \,11''$ approximately. Hence, $6$ radians $= 343^{\circ}38' \,11''$ approximately.