The 30° and 60° references as standards are usually found when operating a lathe.
The tool rest slides on a compound that rotates and has graduations in degrees with 0° being parallel with the axis, 90° is therefore perpendicular to the axis. The tool rest advance is graduated in thousandths of an inch, either in reference to the diameter of the part being machined or in reference to the radius of the part being machined, depending on the brand and model of the lathe. Either way when changing the Depth of Cut (DOC) one can use either the cross slide for direct measurement or one can use the tool post advance. If the tool post is set to 60° and the tool rest is advanced 1 graduation of the dial the change in DOC is 1/2 the reading on the dial. When making facing cuts (reducing the length of the workpiece) setting the compound to 30° will advance the tool into the work 1/2 the reading on the dial.?
The math behind this and other tricky lathe compound settings are far beyond the scope of this thread so please do not drag this on here, there are other forums for that. One in particular you may find interesting (if you are not already a member): /g/atlas-craftsman
Raymond