Why are reference angles necessary in trigonometry.
I've never come across them before.
Apparently, they're the difference between the angle and the nearest multiple of 180° (π).
(so they're always between 0° and 90°)
In other words, trig tables only give you measurements up to 90°, so you find the "reference angle", look up the trig of that in the trig table, and if necessary multiply by minus-one.
Reference angles aren't "necessary". They are convenient, especially back in the years 'BC' (Before Calculators) when you had to look up trig functions in tables. Rather than have tables that extended to, say, 135 degrees, 225 degrees, and 315 degrees, they just went from 0 to 90 degrees so you could look up the "reference angle", 45 degrees, for all those and then apply the correct sign yourself.