Question

Find the degree measures corresponding to the following radian measures:

$\frac{11}{16}$

Answer 1

Convert the unit into degrees

The given quantity is $\frac{11}{16}\mathrm{radian}$.

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

So, $\frac{11}{16}\mathrm{radian}={\left(\frac{11}{16}\times \frac{180}{\mathrm{\pi }}\right)}^{°}$

$\Rightarrow \frac{11}{16}\mathrm{radian}={\left(\frac{11}{4}\times \frac{45}{\mathrm{\pi }}\right)}^{°}$

$\Rightarrow \frac{11}{16}\mathrm{radian}={\left(\frac{11}{4}\times \frac{45}{{\displaystyle \raisebox{1ex}{$22$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}}\right)}^{°}$ $\left[\because \mathrm{\pi }=\frac{22}{7}\right]$

$$\begin{gathered} \Rightarrow \frac{11}{16}\mathrm{radian}={\left(\frac{11\times 45\times 7}{{\displaystyle 4\times 22}}\right)}^{°} \\ \Rightarrow \frac{11}{16}\mathrm{radian}={\left(\frac{1\times 45\times 7}{{\displaystyle 4\times 2}}\right)}^{°} \\ \Rightarrow \frac{11}{16}\mathrm{radian}={\left(\frac{315}{8}\right)}^{°} \\ \Rightarrow \frac{11}{16}\mathrm{radian}=39.375° \end{gathered}$$

Hence, the degree measure of $\frac{11}{16}\mathrm{radian}$ is $39.375°$.