Question

Find the degree measure corresponding to the following radian measures (Use $\pi =\frac{22}{7}$):

(i) $\frac{9\pi }{5}$

(ii) $\frac{-5\pi }{6}$

(iii) ${\left(\frac{180\pi }{5}\right)}^c$

(iv) $(-3{)}^c$

(v) ${11}^c$

(vi) $1^c$

Answer 1

(i) $\frac{9\pi }{5}$
We have,
$\pi$ radians = ${180}^{\circ }$
$1^c={\left\{\frac{180}{\pi }\right\}}^{\circ }$
Now,
${(\frac{9\pi }{5}\times \frac{180}{\pi })}^{\circ }={324}^{\circ }$
(ii) $\frac{-5\pi }{6}$
We hve,
$\pi$ radians = ${180}^{\circ }$
Now,
${\left(\frac{-5\pi }{6}\right)}^c={(\frac{-5\pi }{6}\times \frac{180}{\pi })}^{\circ }=-{150}^{\circ }$
(iii) ${\left(\frac{180\pi }{5}\right)}^c$
We have,
$\pi$ radians = ${180}^{\circ }$
$1^c={\left(\frac{180}{\pi }\right)}^{\circ }$
Now,
${\left(\frac{18\pi }{5}\right)}^c={(\frac{18\pi }{5}\times \frac{180}{\pi })}^{\circ }={648}^{\circ }$
(iv) $(-3{)}^c$
We have,
$\pi$ radians = ${180}^{\circ }$
$1^c={\left(\frac{180}{\pi }\right)}^{\circ }$
Now,
$(-3{)}^c={(-3\times \frac{180}{\pi })}^{\circ }={(\frac{180}{22}\times 7\times -3)}^{\circ }={(-171\frac{9}{11})}^{\circ }=-{171}^{\circ }(\frac{9}{11}\times 60)=-{171}^{\circ }49{}^{\prime }5"$
(v) ${11}^c$
We have,
$\pi$ radians = ${180}^{\circ }$
$1^c={\left(\frac{180}{\pi }\right)}^{\circ }Now,(11{)}^c={(11\times \frac{180}{\pi })}^{\circ }={(11\times 180\times \frac{7}{22})}^{\circ }={630}^{\circ }$
(vi) $1^c$
We have,
$\pi$ radians = ${180}^{\circ }$
$1^c={\left(\frac{180}{\pi }\right)}^{\circ }$
Now,
$1^c={(1\times \frac{180}{\pi })}^{\circ }=\frac{1\times 180\times 7}{22}={57}^{\circ }(\frac{3}{11}\times 60)={57}^{\circ }{16}^{\prime }(\frac{4}{11}\times 60)={57}^{\circ }16{}^{\prime }21"$