A function, continuous in a finite closed interval, can be approximated with a preassigned accuracy by polynomials.
A function of a real variable which is continuous
and has period 
can be approximated by trigonometric polynomials.
Weierstrass's Polynomial Theorem
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References
Szegö, G. Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., p. 5, 1975.Referenced on Wolfram|Alpha
Weierstrass's Polynomial TheoremCite this as:
Weisstein, Eric W. "Weierstrass's Polynomial Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeierstrasssPolynomialTheorem.html