The angles on a hex-grid

The angles on a hex-grid are not sinusoidal, but close to them
As opposed to a circular arc
they are studied as regular divisions of a hex-grid sector
at a given sector radius.

The illustration below shows the angles of a 5-radius sector

These are approximately at intervals of 60/5 = 12 degrees.

Similarly hex-angles can be derived from other sector radii
The illustration below shows the angles at radii upto 6


This property of a hexagonal grid makes it easy to understand design choices
when designing angles.
You get a design-palette to choose from
something that's completely missing from the cartesian grid.