The radian

Up to Year Two we measured angles in sexagesimal degrees: a full angle has $360°$, a right angle $90°$, and so on. It is a convenient choice for everyday life (the number $360$ has many divisors) but entirely arbitrary from a mathematical point of view. In Year Four we move to a more “natural” unit of measure: the radian.

Definition — The radian

Given a circle of radius $R$ and one of its arcs of length $\ell$, the central angle that subtends that arc, measured in radians, is $\alpha = \frac{\ell}{R}.$ The radian is therefore a ratio of lengths: it is dimensionless.

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Topics: Trigonometry
Concepts: Angle · Radian