Question

Convert $6$ radians into degree measure.

Answer 1

We know that $\mathrm{\pi }\mathrm{radian}={180}^{°}$

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

Here we have to convert $6$ radians into degree measure.

$$\begin{gathered} 6\mathrm{radian}=6{\left(\frac{180}{\mathrm{\pi }}\right)}^{°}[\mathrm{\pi }=\frac{22}{7}] \\ 6\mathrm{radian}={\left(\frac{6\times 180\times 7}{22}\right)}^{°} \\ ={(343.94)}^{°} \\ ={343}^{°}+\left(\frac{94\times 60}{100}\right)\text{'} \\ ={343}^{°}+(56.4)\text{'} \\ ={343}^{°}56\text{'}+\left(\frac{4\times 60}{10}\right)" \\ ={343}^{°}56\text{'}24" \end{gathered}$$

Hence, $6radian={343}^{°}56\text{'}24"$