If you have access to modern processors (CPUs, GPUs) then a lookup table makes no sense. The polynomial is faster, more accurate, and needs less space to store precomputed values.
When you peek at the code for computing trig functions in most standard libraries (e.g. C Standard math library in the GNU C compiler), you'll see they typically use a lookup table somewhere in the calculation.
As an example, the LUT will get you in the ballpark of the answer, and then you compute a polynomial to calculate the delta and add the two together.
You can always find a polynomial that is extremely accurate, but it likely will be higher order, etc. A LUT + polynomial is faster. A pure LUT is the fastest, but takes too much memory.
I wouldn't be shocked if lookup tables win on massively it of order CPUs. Of course, I also wouldn't be surprised if it is the it of order nature that makes the polynomial faster.
Would be interesting to see benchmarks. On to my list of things I have a low chance of completing...
