Question

Find the radian measures corresponding to the following degree measures:(i) ${25}^{\circ }$(ii) $-{47}^{\circ }{30}^{\prime }$(iii) ${240}^{\circ }$(iv) ${520}^{\circ }$

Answer 1

We know that , ${180}^{\circ }=\pi$ radian

(i) ${25}^{\circ }=\frac{\pi }{180}\times 25=\frac{5\pi }{36}$ radian

(ii) $-{47}^{\circ }{30}^{\prime }=-47\frac{1}{2}$ degree $[\because 1^{\circ }={60}^{\prime }]=-\frac{95}{2}$ degree

$\therefore -\frac{95}{2}degree=\frac{\pi }{180}\times (-\frac{95}{2})radian=(-\frac{19}{36\times 2})\pi radian=-\frac{19}{72}\pi$ radian

(iii)${240}^{\circ }=\frac{\pi }{180}\times 240=\frac{4}{3}\pi$ radian

(iv) ${520}^{\circ }=\frac{\pi }{180}\times 520radian=\frac{26}{9}\pi$ radian