With the inclusion of floating-point co-processors and faster clock speeds, the polynomial-based methods are now quite fast and have the added benefit of not requiring any table storage. The TI Arm Trig Library uses this method.

The first step in using polynomial approximations is to reduce the range of the input. The bigger the range needed to approximate, the higher order polynomial needed to achieve a specified level of accuracy, which means more computations and slower function performance.

The second step is to compute the approximation for the reduced range and then finally restore the range depending on which quadrant the input was originally in by using trigonometric identities.

There are a number of methods of finding the best polynomials to achieve the lowest error with the fewest terms, but the most commonly used is the minimax approximation algorithm and one version in particular: the Remez algorithm. The Remez algorithm is used to find a polynomial with the least maximum error. This polynomial is called a minimax polynomial. The minimax polynomial is what is used in our optimized trigonometric functions as it is ideal for control applications where worst-case performance is a key care-about.