Question

Convert $4$ radians into degree measure and also convert $-{47}^o{30}^{\prime }$ into radian measure.

Answer 1

(1)

$\pi$ radian $={180}^{\circ }$

$4$ radians $=\frac{180}{\pi }\times 4$ degree

$=\frac{720\times 7}{22}$ degree

$=229\frac{1}{11}$ degree

$={229}^{\circ }+\frac{1\times 60}{11}$ minute

$={229}^{\circ }+5^{\prime }+\frac{5}{11}$ minute

$={229}^{\circ }+5^{\prime }+\frac{5\times 60}{11}$ second

$={229}^{\circ }{5}^{\prime }{27}^{\prime \prime }$ approximately

(2)

${180}^{\circ }=$ $\pi$ radian

$-{47}^{\circ }{30}^{\prime }=-47\frac{1}{2}$ degree

$=-\frac{95}{2}\times \frac{\pi }{180}$ radian

$=-\frac{19\pi }{72}$ radian