Question

Express the radian measure ${\frac{3\pi }{4}}^c$ as sexagesimal measure.

Answer 1

Given:$C=\frac{3\pi }{4}$

We know that $\frac{D}{90}=\frac{2C}{\pi }$

$\frac{D}{90}=\frac{2\times \frac{3\pi }{4}}{\pi }$

$\frac{D}{90}=\frac{6}{4}=\frac{3}{2}$

$D=\frac{3}{2}\times 90$

$\therefore D=3\times {45}^{\circ }={135}^{\circ }$