# How do you convert 73 degrees to radians?

Jul 18, 2015

Angle of $73$ degrees measures $1.2741 \ldots$ in radians

#### Explanation:

By definition, an angle of $1$ radian is an angle that corresponds to an arc equal to a radius in length. Since the circumference of a circle of a radius $R$ equals to $2 \pi R$, there are $2 \pi$ radian in a full circle.

At the same time, there are ${360}^{o}$ in a full circle. Therefore, the correspondence between radians and degrees is based on equality
$2 \pi$ radians = $360$ degrees.

From this we can easily determine the correspondence between $73$ degrees and $X$ radians using a proportion:

$\frac{360}{2 \pi} = \frac{73}{X}$

Solution is
$X = \frac{73 \cdot 2 \pi}{360} = 1.2741 \ldots$ (radians)