Find the degree measures corresponding to the following radian measures \((\text{Use }π=\frac{22}{7}).\)
\(\text{(i) }\frac{11}{16} \,\text{(ii)} -4 \,\text{(iii)}\,\frac{5π}{3}\, \text{(iv)}\, \frac{7π}{6}.\)
\(\text{(i)}\,\frac{11}{16}\)
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°
\(∴\frac{7{\pi}}{6}\text{ radian}=\frac{180}{\pi}×\frac{7{\pi}}{6}\text{degree}= 210°\)