Question

How do you convert \[\pi \] radians to degrees?

Answer 1

Hint:
In this question we will use the concept of the rotation of the wheel that is a complete rotation of the wheel that covers three hundred sixty degrees or two pi radian central angle that means angle can be measured in degree or in radian.

Complete step by step solution:
In this question, we have given an angle measured in radian and we need to convert it into degree. The given angle is $\pi $ radian.
As we know that one radian can be defined as the angle subtended at the center of the circle by the arc which is equal in length to the radius of the circle. So, we can write it in the mathematical form as,
\[ \Rightarrow 1^\circ = \dfrac{{\pi \text{ rad}}}{{180^\circ }}\]
Now, we will calculate the measure of degree in one radian as,
\[ \Rightarrow 1rad = \dfrac{{180^\circ }}{\pi }\]
According to the question we have $\pi $ radian and we need to calculate the measure in degree, so we will multiply above equation by $\pi $ as,
\[ \Rightarrow \left( {1rad} \right)\pi = \left( {\dfrac{{180^\circ }}{\pi }} \right)\pi \]
Now, we will solve the above equation to obtain,
\[\therefore \pi rad = 180^\circ \]

From the above calculation we can conclude that in $\pi rad$ we have $180$ degree.

Note:
As we know that the angle suspended by the arc of a circle can be measured in degree or in radian. As we know that the relation between the length of the arc, central angle suspended by the circle, and the radius of the circle can be written as,
$ \Rightarrow \theta = \dfrac{l}{r}$
Here, the length of the arc is $l$, the radius of the arc is $r$, and the angle suspended by the center of the arc is $\theta $.