Question

Find radian measure corresponding to the degree measure $-{37}^{\circ }{30}^{\prime }$

Answer 1

$\because 1°={60}^{\prime }\Rightarrow {30}^{\prime }={(30\times \frac{1}{60})}^o$ $={0.5}^o$

So, ${37}^o{30}^{\prime }={37}^o+{0.5}^o={37.5}^o$

$\because$ $1^o=\frac{\pi }{180}$ radian

$\therefore$ ${37.5}^o=37.5\times \frac{\pi }{180}$ radian $=\frac{37.5}{180}\pi$ radian $=\frac{5}{24}\pi$ radian.