Definition:Angle/Unit/Degree

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Definition

The degree (of arc) is a measurement of plane angles, symbolized by $^\circ$.

\(\displaystyle \) \(\) \(\displaystyle 1\) $\quad$ degree $\quad$
\(\displaystyle \) \(=\) \(\displaystyle 60\) $\quad$ minutes $\quad$
\(\displaystyle \) \(=\) \(\displaystyle 60 \times 60 = 3600\) $\quad$ seconds $\quad$
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 1 {360}\) $\quad$ full angle (by definition) $\quad$


Value of Degree in Radians

The value of a degree in radians is given by:

$1^\circ = \dfrac {\pi} {180^\circ} \ \mathrm{rad} \approx 0.01745 \ 32925 \ 19943 \ 29576 \ 92 \ldots \ \mathrm{rad}$

This sequence is A019685 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Historical Note

The division of the circle into $360$ degrees originates from the Babylonians, who used a sexagesimal (base $60$) number system for the purposes of mathematics and astronomy.


Degrees are usually the first way of measuring angles taught to mathematics students, usually at grade school.

Conveniently, the most commonly used angles in geometry (e.g. $30^\circ, 45^\circ, 60^\circ$) are all whole numbers when measured in degrees.


Sources

Sources