And you can keep going with this logic, building cos from 0-x by recursively calculating cos from 0-x/2 then mirroring over some line if needed. Eventually you

And you can keep going with this logic, building cos from 0-x by recursively calculating cos from 0-x/2 then mirroring over some line if needed. Eventually you hit machine precision limit aka the base case cos(0) = 1.