Question

Convert $4$ radians into degree measure.

Answer 1

$$\begin{gathered} \mathrm{\pi }\mathrm{radian}=180° \\ 1\mathrm{radian}=\frac{180°}{\mathrm{\pi }} \\ 4\mathrm{radian}={(\frac{180}{\mathrm{\pi }}\times 4)}^{°}(\mathrm{\pi }=\frac{22}{7}) \\ ={(\frac{180}{22/7}\times 4)}^{°} \\ ={\left(229\frac{1}{11}\right)}^{°} \\ =229°+\frac{1\times 60}{11}\mathrm{minute} \\ =229°+5\text{'}+\frac{5}{11}\mathrm{minute} \\ =229°+5\text{'}+\frac{5\times 60}{11}\mathrm{second} \\ =229°5\text{'}27" \end{gathered}$$

Therefore $4radians=229°5\text{'}27"$