Question

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

(i) $\frac{11}{16}$ (ii) -4 (iii) $\frac{5\pi }{3}$ (iv) $\frac{7\pi }{6}$

Answer 1

(i) To convert radian into degree measures, we multiply by $\frac{180}{\pi }$.

$\therefore {\left(\frac{11}{16}\right)}^C={(\frac{11}{16}\times \frac{180\times 7}{22})}^0$

= ${\left(\frac{315}{8}\right)}^0={\left(39\frac{3}{8}\right)}^0$

= ${39}^0{(\frac{3}{8}\times 60)}^{\prime }={39}^0{\left(\frac{45}{2}\right)}^{\prime }$

= ${39}^0{\left(22\frac{1}{2}\right)}^{\prime }={39}^0{22}^{\prime }{(\frac{1}{2}\times 60)}^{\prime \prime }$

= ${39}^0{22}^{\prime }{30}^{\prime \prime }$

(ii) $(-4{)}^C=-{(4\times \frac{180}{\pi })}^0$

=- ${(4\times \frac{180\times 7}{22})}^C=-{\left(\frac{2520}{11}\right)}^0$

=- ${\left(229\frac{1}{11}\right)}^0=-{229}^0{(\frac{1}{11}\times 60)}^{\prime }$

=- ${229}^0{5}^{\prime }27{\frac{3}{11}}^{\prime \prime }$

(iii) ${\left(\frac{5\pi }{3}\right)}^C={(\frac{5\pi }{3}\times \frac{180}{\pi })}^0={300}^0$

(iv) ${\left(\frac{7\pi }{6}\right)}^C={(\frac{7\pi }{6}\times \frac{180}{\pi })}^0={210}^0$