# Convert 4 radians into degree measure and also convert - 47 degree 30′ into radian measure.

To find the respective values.

$$(i) \pi radian =180^{\circ}\\ 4 \text \ radians =\frac{180}{\pi} \times 4 degree\\ =\frac{720 \times 7}{22} degree\\ =\mathbf{2 2 9} \frac{1}{11} degree\\ =\mathbf{2 2 9}^{\circ}+\frac{1 \times 60}{11} minute\\ =\mathbf{2 2 9}^{\circ}+\mathbf{5}^{\prime}+\frac{\mathbf{5}}{\mathbf{1 1}} minute\\ =\mathbf{2 2 9}^{\circ}+\mathbf{5}^{\prime}+\frac{\mathbf{5} \times \mathbf{6 0}}{\mathbf{1 1}} second\\ =\mathbf{2 2 9}^{\circ} \mathbf{5}^{\prime} \mathbf{2 7}^{\prime \prime} \\ (ii) 180^{\circ}=\pi radian\\ -47^{\circ} 30^{\prime}=-47 \frac{1}{2} degree\\ =-\frac{95}{2} \times \frac{\pi}{180} radian\\ =-\frac{19 \pi}{72} radian$$