Question

Find the degree measures corresponding to the following radian measures $(\text{Use }π=\frac{22}{7}).$

$\text{(i) }\frac{11}{16} \,\text{(ii)} -4 \,\text{(iii)}\,\frac{5π}{3}\, \text{(iv)}\, \frac{7π}{6}.$

Answer 1

$\text{(i)}\,\frac{11}{16}$

We know that π radian = 180°

$=\frac{11}{16} \,radain=\frac{180}{\pi}×\frac{11}{16}\text{degree}= \frac{45×11}{{\pi}x4}\text{degree}$

$=\frac{45×11×7}{22×4}\text{degree}=\frac{315}{8}\text{degree}$

$39\frac{3}{8}\,\text{degree}$

$39^°+\frac{3×60}{8}\text{minutes}....[1^°=60']$

$=39^°+22'+\frac{1}{2}\,\text{minutes}$

$=39^°22'30''.....[1'=60'']$

---

$\text{(ii)}\,-4$

We know that π radian = 180°

$-4\,radian=\frac{180}{\pi}×\text{degree}=-229\frac{1}{11}\text{degree}$

$=\frac{-2520}{11}\,degree\,=-229\frac{1}{11}\\.degree$

$=-229^°+\frac{1×60}{11}\,minutes....[1^°=60']$

$=-229^°+5'+\frac{5}{11}\,\text{minutes}$

$=-229^°5'27''.....[1'=60'']$

---

$(iii)\,\frac{5\pi}{3}$

We know that π radian = 180°

$∴\frac{5{\pi}}{6} \text{ radian}=\frac{180}{\pi}×\frac{5{\pi}}{6}\text{degree}= 300°$

---

$(iv)\,\frac{7\pi}{6}$

We know that π radian = 180°

$∴\frac{7{\pi}}{6}\text{ radian}=\frac{180}{\pi}×\frac{7{\pi}}{6}\text{degree}= 210°$