Question

Find the radian measures corresponding to the following degree measures :
$\left(1\right){25}^{\circ }$
$\left(2\right)-{47}^{\circ }{30}^{\prime }$
$\left(3\right){240}^{\circ }$
$\left(4\right){520}^{\circ }$

Answer 1

Using formula ${180}^{\circ }=\pi$ radian
$\therefore {25}^{\circ }=\frac{\pi }{180}\times 25$ radian
$=\frac{5\pi }{36}$ radian
$\therefore {25}^{\circ }=\frac{5\pi }{36}$ radian

Using formula $1^{\circ }={60}^{\prime }$
$-{47}^{\circ }{30}^{\prime }=-47\frac{30}{60}$ degree
$=-47\frac{1}{2}$ degree
$=-\frac{95}{2}$ degree
Using formula ${180}^{\circ }=\pi$ radian
$\therefore -\frac{95}{2}\text{degree}=-\frac{95}{2}\times \frac{\pi }{180}$ radian
$=-\frac{19\pi }{72}$ radian
$\therefore -{47}^{\circ }{30}^{\prime }=-\frac{19\pi }{72}$ radian

Using formula ${180}^{\circ }=\pi$ radian
$\therefore {240}^{\circ }=240\times \frac{\pi }{180}\times 25$ radian
$=\frac{4\pi }{3}$ radian
$\therefore {240}^{\circ }=\frac{4\pi }{3}$ radian

Using formula ${180}^{\circ }=\pi$ radian
$\therefore {520}^{\circ }=520\times \frac{\pi }{180}$ radian
$=\frac{26\pi }{9}$ radian
$\therefore {520}^{\circ }=\frac{26\pi }{9}$ radian