Definition:Angular Measure/Degree

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Definition

The degree (of angle) is a measurement of plane angles, symbolized by $\degrees$.

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


Value of Degree in Radians

The value of a degree in radians is given by:

$1 \degrees = \dfrac {\pi} {180} \radians \approx 0 \cdotp 01745 \, 32925 \, 19943 \, 29576 \, 9236 \ldots \radians$

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


Also known as

Degrees of angle are also referred to as sexagesimal measure.

See sexagesimal notation for further explanation.

Some sources use the terminology degree measure.


A degree of angle is also known as a degree of arc.

This term has a specific definition which is subtly different from the concept of a degree of angle, and so its use in this context on $\mathsf{Pr} \infty \mathsf{fWiki}$ is discouraged.


Also see

  • Results about degrees of angle can be found here.


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 (for example $30 \degrees$, $45 \degrees$, $60 \degrees$) are all whole numbers when measured in degrees.


Technical Note

The $\LaTeX$ code for \(\degrees\) is \degrees .


Sources

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