The unit circle

Definition — The unit circle

The unit circle is the circle centred at the origin with radius $1$ in the Cartesian plane: $\mathcal{C}_{\text{gon}}:\quad x^2 + y^2 = 1.$

The choice of radius $1$ is strategic: the length of an arc coincides with the radian measure of the corresponding central angle. This allows an angle to be represented geometrically, as a path along the unit circle starting from a reference point.

Links

Topics: Trigonometry
Concepts: Unit circle