It's great for hardware implementations, because it's simple and you get good/excellent accuracy. I wouldn't be surprised if that's still how modern x86-64 CPUs compute sin, cos, etc.

That said, last time I had to do that in software, I used Taylor series. Might not have been an optimal solution.

EDIT:

AMD's Zen 4 takes 50-200 cycles (latency) to compute sine. I think that strongly suggests AMD uses CORDIC. https://www.agner.org/optimize/instruction_tables.pdf page 130.

Same for Intel, Tiger Lake (Intel gen 11) has 60-120 cycles of latency. Page 353.

I'd guess usually ~50 cycles for Zen 4 (and ~60 for Intel) for float32, float64/float80 datatype. Denormals might also cost more cycles.