Hi Andreas,
you should specify the following points, that impact the type of approximation and the resulting complexity:
a) which is the range of x over which you want the approximation
b) what are the allowed errors and what type of specification do they have (i.e.: maximum absolute errors, maximum relative errors)
c) what resources are allowed (processor or FPGA, multiplier, huge memory, etc.)
d) other constraints?
Normally, a polynomial approximation is ok for this type of function. It requires only multiplications and sums.
Another possibility is using look up tables and interpolation between values of the table.
Cos and Sin are very time consuming and, by the way, they are frequently implemented using piecewise polynomial approximations.
Regards
Z