Question

How do you convert $\dfrac{4 \pi }{3}$ into degrees?

Answer 1

Hint: In this problem we need to convert the given radians into degrees. For this, we have to know about the relation between radians and degrees. We have the relation between radians and degrees as $180{}^\circ =1\pi $. From this equation, we will calculate the value of $\dfrac{4\pi }{3}$ in degrees. For this, we will first multiply the relation we have with $4$ on both sides to calculate the value of $4\pi $. After simplifying the equation, we will get the value of $4\pi $. Now we will divide the value of $4\pi $ with $3$ to find the value of $\dfrac{4\pi }{3}$. After simplifying this equation also, we will get the value of $\dfrac{4\pi }{3}$ which is our required value.

Complete Step by Step Procedure:
Given angle $\dfrac{4\pi }{3}$ radians.
We need to convert the above radians value into degrees. For this, we are going to use the relation between the radians and degrees which is
$1\pi =180{}^\circ $
Multiplying the above equation with $4$ on both sides to get the value of $4\pi $. Then we will get
$4\times 1\pi =4\times 180{}^\circ $
Simplifying the above equation, then we will have the value of $4\pi $ as
$4\pi =720{}^\circ $
Dividing the above equation with $3$ into both sides to get the value of $\dfrac{4\pi }{3}$. Then we will get
$\dfrac{4\pi }{3}=\dfrac{720{}^\circ }{3}$
Simplifying the above equation, then we will have the value of $\dfrac{4\pi }{3}$ as
$\dfrac{4\pi }{3}=240{}^\circ $

Hence the value of $\dfrac{4\pi }{3}$ radians in degrees is $240{}^\circ $.

Note:
We can also follow another method to calculate the value of $\dfrac{4\pi }{3}$. We will first divide the equation $1\pi =180{}^\circ $ with $3$ to get the value of $\dfrac{\pi }{3}$. Then we will get the value of $\dfrac{\pi }{3}$ as
$\dfrac{1\pi }{3}=\dfrac{180{}^\circ }{3}$.