Question

Convert $\dfrac{{2\pi }}{3}$ radians into degrees?

Answer 1

Hint: Here we have to convert radian to degree. For this conversion we will use a relation between radians and degrees. The relation is $X{\text{ }}radians = \dfrac{{180X}}{\pi }^\circ$ now on putting the value of X in radians and further simplify it, we get the required answer in radians.

Complete step by step solution:
In the given question we have to convert $\dfrac{{2\pi }}{3}$ radians into degrees.
To convert we use the relation between radians and degrees.
The relation between degrees and radians
$X{\text{ }}radians = \dfrac{{180X}}{\pi }^\circ$
From the above relation it is clear that $1$ radian is equal to $\dfrac{{180}}{\pi }^\circ$.
So for getting $\dfrac{{2\pi }}{3}$ radians into degrees we have to put $\dfrac{{2\pi }}{3}$in the place of ‘X’
On putting this value in the above relation we get
$\dfrac{{2\pi }}{3}radians = \dfrac{{2\pi }}{3} \times \dfrac{{180}}{\pi }^\circ$
On further simplify we get
$\dfrac{{2\pi }}{3}radians = {120^ \circ }$
Therefore, the $\dfrac{{2\pi }}{3}$ radians can be written as ${120^\circ }$.

Note:
Degrees and radians are two different units that are used for the measurement of the angles. The measure of the angle generally denoted in degrees having the symbol $( \circ )$.
An angle can be measured by two units that are degrees and radian. But for solving this type of problem we should remember conversion formulas.
> To remember this we should know that $\pi $ radian is always equal to $180$ degrees. So we can say that $1$ degree is equal to $\dfrac{\pi }{{180}}$ radians and $1$ radian is equal to $\dfrac{{180}}{\pi }$degree.
> Therefore for converting an angle from radians to degrees we need to multiply the radians by$\dfrac{{180}}{\pi }$ whereas for converting from degrees to radians we need to multiply the degrees by$\dfrac{\pi }{{180}}$.
> In this type of problem we also put the value of $\pi $ $\left( {\pi = \dfrac{{22}}{7}{\text{ }}or{\text{ }}3.14} \right)$ to get the required answer in degrees, minutes and seconds.