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Minute of Time

The minute is a derived unit of time.

$1$ minute $= 60$ seconds.

Minute of Arc

The minute (of arc) is a measurement of plane angles, symbolized by $'$.

\(\ds \) \(\) \(\ds 1\) minute
\(\ds \) \(=\) \(\ds 60\) seconds
\(\ds \) \(=\) \(\ds \dfrac 1 {60}\) degree of arc (by definition)

Linguistic Note

The word minute, in the context of the measurement both of time and of angle, derives from its initial definition as a minute part of an hour or of a degree of arc.

In this context the word minute (meaning: the aggregation of $60$ seconds) is pronounced min-it.

The word minute (as used in the phrase minute part) is pronounced my-nyoot and means small.

So the fact that the two words are spelt identically is not a coincidence.