"One of the best ways to calculate sin and cos is CORDIC" This is extremely false. Cordic is 1 bit per iteration, while polynomials (Chebyshev or minmax) converge exponentially faster.
You are of course right about the speed, when a fast hardware multiplier is available for the computation of the polynomials.
On the other hand with CORDIC it is extremely easy to reach any desired precision, and in cheap hardware it does not require multipliers.
So CORDIC may be considered as "one of the best ways" depending on how "best" is defined.
Even when developing a polynomial approximation for the fast evaluation of a trigonometric function, it may be useful to use an alternative evaluation method by CORDIC, in order to check that the accuracy of the polynomial approximation is indeed that expected, because for CORDIC it is easier to be certain that it computes what it is intended.
On the other hand with CORDIC it is extremely easy to reach any desired precision, and in cheap hardware it does not require multipliers.
So CORDIC may be considered as "one of the best ways" depending on how "best" is defined.
Even when developing a polynomial approximation for the fast evaluation of a trigonometric function, it may be useful to use an alternative evaluation method by CORDIC, in order to check that the accuracy of the polynomial approximation is indeed that expected, because for CORDIC it is easier to be certain that it computes what it is intended.