# Find the radian measure corresponding to the following degree measures:

Question:

Find the radian measure corresponding to the following degree measures:

(i) 300°

(ii) 35°

(iii) −56°

(iv) 135°

(v) −300°

(vi) 7° 30'

(vii) 125° 30'

(viii) −47° 30'

Solution:

We have :

$180^{\circ}=\pi \mathrm{rad}$

$\therefore 1^{\circ}=\frac{\pi}{180} \mathrm{rad}$

(i) $300^{\circ}$

$=\left(300 \times \frac{\pi}{180}\right)$

$=\frac{5 \pi}{3} \mathrm{rad}$

(ii) $35^{\circ}$

$=35 \times \frac{\pi}{180}$

$=\frac{7 \pi}{36} \mathrm{rad}$

(iii) $-56^{\circ}$

$=-\left(56 \times \frac{\pi}{180}\right)$

$=-\frac{14 \pi}{45} \mathrm{rad}$

(iv) $135^{\circ}$

$=135 \times \frac{\pi}{180}$

$=\frac{3 \pi}{4} \mathrm{rad}$

$(\mathrm{v})-300^{\circ}$

$=-\left(300 \times \frac{\pi}{180}\right)$

$=-\frac{5 \pi}{3} \mathrm{rad}$

(vi) $30^{\prime}=\left(\frac{1}{2}\right)^{\circ}$

$\therefore 7^{\circ} 30^{\prime}=\left(7 \frac{1}{2}\right)^{\circ}$

$=\left(\frac{15}{2}\right)^{\circ}$

$=\frac{15}{2} \times \frac{\pi}{180}$

$=\frac{\pi}{24} \mathrm{rad}$

(vii) $30^{\prime}=\left(\frac{1}{2}\right)^{\circ}$

$\therefore 125^{\circ} 30^{\prime}=\left(125 \frac{1}{2}\right)^{\circ}$

$=\left(\frac{251}{2}\right)^{\circ}$

$=\frac{251}{2} \times \frac{\pi}{180}$

$=\frac{251 \pi}{360} \mathrm{rad}$

(viii) $30^{\prime}=\left(\frac{1}{2}\right)^{\circ}$

$\therefore 47^{\circ} 30^{\prime}=-\left(47 \frac{1}{2}\right)^{\circ}$

$=-\left(\frac{95}{2}\right)^{\circ}$

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

$=-\frac{19 \pi}{72}$ rad