Question

Find the degree measure of $\frac{1}{4}\mathrm{radian}$.

Answer 1

Convert the unit into degrees

The given quantity is $\frac{1}{4}\mathrm{radian}$.

As we know, $\mathbf{1}\mathbf{}\mathbf{radian}\mathbf{}\mathbf{=}{\left(\frac{180}{\pi }\right)}^{\mathbf{°}}$

So, $\frac{1}{4}\mathrm{radian}={\left(\frac{1}{4}\times \frac{180}{\mathrm{\pi }}\right)}^{°}$

$$\begin{gathered} \Rightarrow \frac{1}{4}\mathrm{radian}={\left(\frac{1}{1}\times \frac{45}{\mathrm{\pi }}\right)}^{°} \\ \Rightarrow \frac{1}{4}\mathrm{radian}={\left(\frac{45}{\mathrm{\pi }}\right)}^{°} \end{gathered}$$

$\Rightarrow \frac{1}{4}\mathrm{radian}=\frac{45°}{{\displaystyle \raisebox{1ex}{$22$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}}$ $\left[\because \mathrm{\pi }=\frac{22}{7}\right]$

$$\begin{gathered} \Rightarrow \frac{1}{4}\mathrm{radian}={\left(\frac{7\times 45}{{\displaystyle 22}}\right)}^{°} \\ \Rightarrow \frac{1}{4}\mathrm{radian}={\left(\frac{315}{{\displaystyle 22}}\right)}^{°} \\ \Rightarrow \frac{1}{4}\mathrm{radian}=\left(14.3181818..\right)° \\ \Rightarrow \frac{1}{4}\mathrm{radian}\approx 14.32° \end{gathered}$$

Hence, the degree measure of $\frac{1}{4}\mathrm{radian}$ is $14.32°$.