I looked for other people that had approximated cos() and sin() and I came across this answer:
dtb's answer to "Fast Sin/Cos using a pre computed translation array"dtb's answer to "Fast Sin/Cos using a pre computed translation array"
Basically he computed that the math.sin() function from the math library was faster than using a look-up table of values. But from what I can tell, this was computed on a PC.
Arduino has a math library included that can calculate sin() and cos().