Question

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

Answer 1

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.