Question

Express in radians ${47}^{\circ }{25}^{\prime }36"$

• A. $\frac{3472}{38921}{\pi }^c$
• B. $\frac{3247}{13562}{\pi }^c$
• C. $\frac{3557}{13500}{\pi }^c$
• D. $\frac{6582}{25700}{\pi }^c$

Answer 1

The correct option is C $\frac{3557}{13500}{\pi }^c$

${47}^{\circ }{25}^{\prime }\left(\frac{36}{60}\right)={47}^{\circ }\left(25\frac{3}{5}\right)$
$={47}^{\circ }\left(\frac{128}{5}\right)={47}^{\circ }{(\frac{128}{5}\times \frac{1}{60})}^{\circ }={\left(47\frac{32}{75}\right)}^{\circ }$
$={\left(\frac{3557}{75}\right)}^{\circ }=\frac{3557}{75}\times \frac{{\pi }^c}{180}=\frac{3557}{13500}{\pi }^c$$