Question

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

Answer 1

Hint: In the above question we were asked to convert $\dfrac{\pi }{3}$ radian into degrees. Radian is a measurement based on the radius of the circle. Also, in a half-circle, there are $\pi$ radians that is ${180^ \circ }$. You can convert degrees into radian by multiplying it to $(\dfrac{{180}}{\pi })$. So let us see how we can solve this problem.

Complete step by step solution:
In the given question we were asked to convert $\dfrac{\pi }{3}$ radian into degrees.
We can convert radian into degrees by multiplying it to $(\dfrac{{180}}{\pi })$. Therefore, multiplying $\dfrac{\pi }{3}$ radian with $(\dfrac{\pi }{{180}})$
 $= \dfrac{\pi }{3} \times (\dfrac{{180}}{\pi })$ degrees
 $= 60$ degrees

Therefore, $\dfrac{\pi }{3}$ radians into the degree is ${60^ \circ }$.

Note:
In the above solution we get ${60^ \circ }$ as the radian conversion of $\dfrac{\pi }{3}$. Note that the value of $\pi$ is 3.141 which we get after dividing 22 with 7. Also, for converting degrees into radians we need to multiply the degree with $(\dfrac{\pi }{{180}})$ but for converting radian into degrees we need to multiply radian with $(\dfrac{{180}}{\pi })$. And the value of $\pi$ is fixed which is 3.141 or $\dfrac{{22}}{7}$. Also, in the solution we cancelled $\pi$ and 3 times 60 is 180. So we get 60 degrees.