Question

How many radians is $2\mathrm{\pi }$?

Answer 1

Find $2\mathrm{\pi }$ in terms of radian

A radian is the angle made by an arc of the circle whose arc length is equal to the radius of the circle.

If we consider the circumference of the circle then,

Angle in radians$=\frac{circumference}{radius}$

$\Rightarrow$Angle in radians$=\frac{2\mathrm{\pi r}}{r}=2\mathrm{\pi }$

We know that the angle subtended by the center of the circle is ${360}^{\circ }$

$\Rightarrow$$2\mathrm{\pi }\mathrm{rad}={360}^{\circ }$

$\Rightarrow$ $1rad=\frac{180}{\mathrm{\pi }}\approx 57.3°$

Hence, $2\mathrm{\pi }\mathrm{rad}={360}^{\circ }=6.283rad$