Question

Match the following angle in degree measure with corresponding angles in radians.

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{4}$

Answer 1

We know the relation:
$\frac{D}{{180}^{\circ }}=\frac{R}{\pi }$
Where, $D$ is the measure of angles in degrees and $R$ is the measure of angle in radians.

$a.D={30}^{\circ }\Rightarrow \frac{{30}^{\circ }}{{180}^{\circ }}=\frac{R}{\pi }$

$\Rightarrow \frac{1}{6}\times \pi =R\Rightarrow R=\frac{\pi }{6}$

$b.D={45}^{\circ }\Rightarrow \frac{{30}^{\circ }}{{180}^{\circ }}=\frac{R}{\pi }$

$\Rightarrow \frac{1}{4}\times \pi =R\Rightarrow R=\frac{\pi }{4}$

$c.D={60}^{\circ }\Rightarrow \frac{{30}^{\circ }}{{180}^{\circ }}=\frac{R}{\pi }$

$\Rightarrow \frac{1}{3}\times \pi =R\Rightarrow R=\frac{\pi }{3}$