You wouldn't use 19 place trig values when dealing with 19 place variables. Can you guess why?

if my radius is 1234mm
and the sine of 60 degrees to 3 places is 866 / 1000
I can accurately calculate 1234 * 866 / 1000 as long as I have enough places to hold the intermediate results.

I promise you that these techniques have been worked out and used extensively decades ago.

You don't have to table every possible angle. You only have to get close enough to interpolate with a required degree of precision that BTW, it's possible to beat what IEEE floating point can give you. If you need large tables then interface an SD card and maybe learn to use index files.

Generally when your code is doing the same set of calculations over and over you can precalculate chunks to all of that into one or more tables, early flight sims worked at all that way. Charles Moore the astronomer was aiming big telescopes to track objects using tables for fast fourier calcs before 1960 that way. It depends on what you're doing and your own ability to work out algorithms.

There are BCD techniques that allow math to arbitrarily high precisions, even beyond 100 places. They are completely accurate. Most hand calculators in the past used them and some or all still might.

Do what you want but realize that there's more than one viable way to skin a cat.