Question

Match the following angles in radians with their corresponding angles in degrees.

• A. ${75}^{\circ }$
• B. ${315}^{\circ }$
• C. ${57}^{\circ }{17}^{\prime }{24}^{\prime \prime }$
• D. ${220}^{\circ }$

Answer 1

We know the relation:
$\frac{D}{{180}^{\circ }}=\frac{R}{\pi }$

$\Rightarrow D={180}^{\circ }\times \frac{R}{\pi }$
Where $R$ is the angle in radians and $D$ is the angles in degrees.
$\left(a\right)R=1\text{radians}\Rightarrow D={180}^{\circ }\times \frac{1}{\pi }$
$\Rightarrow R=\frac{{180}^{\circ }}{\pi }={57.29}^{\circ }$
Now, ${57.29}^{\circ }={57}^{\circ }+{0.29}^{\circ }$
$\Rightarrow {0.29}^{\circ }=0.29\times {60}^{\prime }={17.40}^{\prime }={17}^{\prime }+{0.4}^{\prime }$
$\Rightarrow {0.4}^{\prime }=0.4\times {60}^{\prime \prime }={24}^{\prime \prime }$
$\Rightarrow 1\text{radian}={57}^{\circ }{17}^{\prime }{24}^{\prime \prime }$

$\left(b\right)\frac{5\pi }{12}\Rightarrow D={180}^{\circ }\times \frac{5\pi }{12\times \pi }$
$\Rightarrow D={180}^{\circ }\times \frac{5}{12}={75}^{\circ }$

$\left(c\right)\frac{7\pi }{4}\Rightarrow D={180}^{\circ }\times \frac{7\pi }{4\times \pi }$
$\Rightarrow D={180}^{\circ }\times \frac{7}{4}={315}^{\circ }$

$\left(d\right)\frac{11\pi }{9}\Rightarrow D={180}^{\circ }\times \frac{11\pi }{9\times \pi }$
$\Rightarrow D={180}^{\circ }\times \frac{11}{9}={220}^{\circ }$