Question

Express the following angle into radians :
${50}^o{37}^{{}^{\prime }}{30}^{\prime \prime }$

Answer 1

$30seconds=\left(\frac{30}{60}\right)minutes$

$37minutes30seconds=(37+\frac{1}{2})=\left(\frac{75}{2}\right)minutes={\left(\frac{75}{2\times 60}\right)}^o={\left(\frac{5}{8}\right)}^o$

${50}^{o}37minutes30seconds={(50+\frac{5}{8})}^o={\left(\frac{405}{8}\right)}^o$

${\left(\frac{405}{8}\right)}^o=\frac{\pi }{180}\times \frac{405}{8}radians=\frac{9\pi }{32}radians$