Find the radian measures corresponding to the following degree measures:

Solution:

(i) $25^{\circ}$

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

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

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

$-47^{\circ} 30^{\prime}=-47 \frac{1}{2}$ degree $\left[1^{\circ}=60^{\prime}\right]$

$=\frac{-95}{2}$ degree

Since $180^{\circ}=\pi$ radian

$\frac{-95}{2}$ deg ree $=\frac{\pi}{180} \times\left(\frac{-95}{2}\right)$ radian $=\left(\frac{-19}{36 \times 2}\right) \pi$ radian $=\frac{-19}{72} \pi$ radian

$\therefore-47^{\circ} 30^{\prime}=\frac{-19}{72} \pi$ radian

(iii) $240^{\circ}$

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

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

(iv) $520^{\circ}$

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

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