> I don't just mean linear or poly graphs etc, but using sections of sin, cos, tan, tanh, sin^(2) etc.
People fit all sorts of functions to data all the time. If you e.g. know you have data that should be some kind of sine wave you can do a least squares fit to find the best amplitude, wavelength, and phase-offset to use. (Or the same for whatever other kind of function.)
But unless you have some a priori knowledge of the function, it generally makes no sense to fit it via some large collection of other functions.
In practice people approximate arbitrary functions by fitting polynomials or rational functions (ratios of polynomials), because those are convenient to work with and computationally tractable (they involve only basic arithmetic), with a well developed theory. But if you e.g. have a function with a square-root singularity, a polynomial or rational approximant might be slow to converge; then you can try to approximate your function as the product of a square root and a rational function. Etc.
If the domain of your function is a periodic interval, you should use trigonometric polynomials (a function with terms like *a* sin(*kx*) or *b* cos(*mx*) for integers *k*, *m*) or trigonometric rational functions, instead.