Question

How do you convert $\frac{2\mathrm{\pi }}{3}$into degrees?

Answer 1

Convert radian into degrees:

Given angle in degree, $\frac{2\mathrm{\pi }}{3}$.

We know that, $1\mathrm{radian}$ is equal to $\frac{180°}{\mathrm{\pi }}$.

To convert radians into degrees, multiply the given angle by $\frac{180°}{\mathrm{\pi }}$.

Multiply $\frac{2\mathrm{\pi }}{3}$ by $\frac{180°}{\mathrm{\pi }}$.

$$\begin{gathered} \frac{2\mathrm{\pi }}{3}\times \frac{180°}{\mathrm{\pi }}=\frac{2\times 180°}{3} \\ \therefore \frac{2\mathrm{\pi }}{3}\times \frac{180°}{\mathrm{\pi }}=120° \end{gathered}$$

Hence, the required value is $120°$.