On: An Interactive Introduction to Fourier Transforms

[EmilioMartinez]

>sines and cosines are polynomials evaluated on the complex unit circle

Could you explain further?

[enriquto → EmilioMartinez]

If you evaluate the complex function f(x)=z^n on the unit circle z=exp(it), you obtain cos(nt)+i sin(nt). Thus Fourier series are "just" Taylor series evaluated on the unit circle.