Question

Find the degree measures corresponding to the following radian measures: $(\text{use}\pi =\frac{22}{7})$
$\left(i\right)\frac{11}{16}$ radian
$\left(ii\right)-4$ radian
$\left(iii\right)\frac{5\pi }{3}$ radian
$\left(iv\right)\frac{7\pi }{6}$ radian

Answer 1

(i) Using formula $\pi$ radian $={180}^{\circ }$
$\therefore \frac{11}{16}$ radian $=\frac{180}{\pi }\times \frac{11}{16}$ degree
$=\frac{45\times 11}{\pi \times 4}$ degree
$=\frac{45\times 11\times 7}{4\times 22}$ degree
$=\frac{315}{8}$ degree $\{\because \pi =\frac{22}{7}\}$
$=39\frac{3}{8}$ degree
$={39}^{\circ }\frac{3\times 60}{8}$ minutes
$\{\because 1^{\circ }={60}^{\prime }\}$
$={39}^{\circ }+{22}^{\prime }+\frac{1}{2}$ minutes
$={39}^{\circ }{22}^{\prime }{30}^{\prime \prime }\{\because 1^{\prime }=60"\}$
$\therefore \frac{11}{16}$ radian = ${39}^{\circ }{22}^{\prime }30"$

(ii) Using formula $\pi$ radian $={180}^{\circ }$
$\therefore -4$ radian =$-4\times \frac{180}{\pi }$ degree
$=\frac{180\times 7\times (-4)}{22}$ degree $\{\because \pi =\frac{22}{7}\}$
$=\frac{-2520}{11}$ degree $=-229\frac{1}{11}$ degree
$=-({229}^{\circ }+\frac{1\times 60}{11})$ minutes $\{\because 1^{\circ }={60}^{\prime }\}$
$=-({229}^{\circ }+5^{\prime }+\frac{5}{11})$ minutes $\{\because 1^{\prime }=60"\}$
$=-{229}^{\circ }{5}^{\prime }27"$
$\therefore -4$ radian $=-{229}^{\circ }{5}^{\prime }{27}^{\prime \prime }$ approximately

(iii) Using formula $\pi$ radian $={180}^{\circ }$
$\therefore \frac{5\pi }{3}$ radian $=\frac{180}{\pi }\times \frac{5\pi }{3}$ degree
$={300}^{\circ }$
$\therefore \frac{5\pi }{3}$ radian $={300}^{\circ }$

(iv) Using formula $\pi$ radian $={180}^{\circ }$
$\therefore \frac{7\pi }{6}$ radian $=\frac{180}{\pi }\times \frac{7\pi }{6}$ degree
$={210}^{\circ }$
$\therefore \frac{7\pi }{6}$ radian $={210}^{\circ }$