Definition: The radian is the coherent unit for plane angle. One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius. It is also the unit for phase angle. For periodic phenomena, the phase angle increases by 2π rad in one period.
Source: SI Brochure 9th Ed. 2019, p 137
The radian was formerly an SI supplementary unit, but this category was abolished in 1995.
The SI unit of angular velocity and angular frequency is radian per second, whereas the SI unit of frequency is hertz.
It is particularly important to carefully distinguish frequencies from angular frequencies, because by definition their numerical values differ by a factor of 2π.