Question

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

Answer 1

We know that $\pi$ radian $={180}^{\circ }$
(i) $\therefore \frac{11}{16}radian=\frac{180}{\pi }\times \frac{11}{16}degree=\frac{45\times 11\times 7}{22\times 4}degree=39\frac{3}{8}$ degree
$={39}^{\circ }+\frac{3\times 60}{8}$ minutes $,[\because 1^{\circ }={60}^{\prime }]$
$={39}^{\circ }+{22}^{\prime }+\frac{1}{2}$ minutes
$={39}^{\circ }{22}^{\prime }{30}^{\prime \prime }$ $,[\because 1^{\prime }={60}^{\prime \prime }]$

(ii)$\therefore -4radian=\frac{180}{\pi }\times (-4)degree=\frac{180\times 7(-4)}{22}degree=-229\frac{1}{11}$ degree

$=-{229}^{\circ }+\frac{1\times 60}{11}$ minutes $,[\because 1^{\circ }={60}^{\prime }]$

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

$=-{229}^{\circ }{5}^{\prime }{27}^{\prime \prime }$ $,[\because 1^{\prime }={60}^{\prime \prime }]$

(iii)$\therefore \frac{5\pi }{3}radian=\frac{180}{\pi }\times \frac{5\pi }{3}degree$

$={300}^{\circ }$

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