Question

Find the radian measures corresponding following degree measures.
$5^{\circ }{37}^{\prime }{30}^{\prime \prime }$

Answer 1

Consider given the angle,

$\Rightarrow 5^0{37}^{{}^{\prime }}{30}^{{}^{\prime \prime }}$

$\because 1^{{}^{\prime }}={60}^{{}^{\prime \prime }}$

$\Rightarrow \therefore 5^0{37}^{{}^{\prime }}\frac{30}{60}$

$\Rightarrow 5^0{37}^{{}^{\prime }}\frac{1}{2}$

$\Rightarrow 5^0\frac{75}{2}$

$\Rightarrow \because 1^0={60}^{{}^{\prime }}$

$\Rightarrow 5^0\frac{75}{2\times 60}$

$\Rightarrow 5^0\frac{5}{8}$

$\Rightarrow {\left(\frac{45}{8}\right)}^0$

Now,

$\Rightarrow \frac{45}{8}\times \frac{\pi }{180}$

$\Rightarrow \frac{\pi }{32}$

Hence this is the answer.