As you probably know functions can be represented as a infinite series. For example f(x) = cosx can be represented as this. My question is if this is every used practically in programming for any type of application. I know it can be used I was just wondering if it actually is for serious projects.
Aside from infinite series, there are other representations for functions which can be useful for computing approximations. Asymptotic series, identities involving other "elementary" functions, and interpolation in a table of values are all used in different contexts. Take a look at Abramowitz & Stegun "Handbook of Mathematical Functions" to get an idea of the variety of possibilities. Also look for the source code for popular libraries or systems such as R, Numpy, Scipy, or Octave to see what approaches have been used by the authors of that software.
Specifically about series approximations for trigonometric functions, I think that might be a reasonable thing to do, but only if the range of the argument is reduced (via identities) so that it is as small as possible.
Approximation of functions is a great topic; good luck and have fun.
