How to calculate approximation error of trigonometric functions

[qukolhavi]

I recently reread my undergrad Calculus book and read in the section on Taylor series that Taylor polynomials are used in programming languages to approximate trigonometric functions. I have a few questions:

• Are Taylor polynomials actually used or is there a better method? (Skepsis comes from the number of divisions in these polynomials although I guess you could precompute most)

• If yes, then of which degree is the polynomial?

• How do you measure the approximation error compared to the real function? I can imagine that an approximation can be compared to one that is even more precise due to a higher degree. But that comparison would be between two approximations.

[ace589]

My understanding is that:

On embedded system implementations CORDIC algorithms are used.  Entire courses exist on this subject.

At larger scale, software libraries typically will store the results in 1/2 degrees in a table and anything smaller is interpolated between those 1/2 degree increments.