Question

Express ${104}^{\circ }{30}^{\prime }$ in radians.

Answer 1

${104}^{\circ }{30}^{\prime }={104}^{\circ }+\frac{{36}^{\circ }}{60}$

$={104}^{\circ }+\frac{3^{\circ }}{5}$

$=\frac{523}{5}$ degrees

$\because$ ${180}^{\circ }=\pi$ radians

$\Rightarrow$ $1^{\circ }=\frac{\pi }{180}$ radians

$\therefore \frac{523}{5}$ degrees $=\frac{\pi }{180}\times \frac{523}{5}$ radians

$=\frac{523\pi }{900}$ radians