Question

Find the radian measures corresponding to the following degree measures:

(i) ${25}^0$

(ii) $-{47}^0{30}^{\prime }$

(iii) ${240}^0$

(iv) ${520}^0$

Answer 1

(i) To convert degree measures into radians,

we multiply by $\frac{\pi }{180}$

$\therefore {25}^0={(25\times \frac{\pi }{180})}^c={\left(\frac{5\pi }{36}\right)}^c$

(ii) $-{47}^0{30}^{\prime }=-{\left(47\frac{30}{60}\right)}^c=-{\left(\frac{95}{2}\right)}^0$

=$-{(\frac{95}{2}\times \frac{\pi }{180})}^c=-{\left(\frac{19\pi }{72}\right)}^c$

(iii) ${240}^0={(240\times \frac{\pi }{180})}^c={\left(\frac{4\pi }{3}\right)}^3$

(iv) ${520}^0={(520\times \frac{\pi }{180})}^c={\left(\frac{26\pi }{9}\right)}^c$