Trigonometric polynomails dense in $C(T)$ with period $1$ instead of $2\pi$

Question

It is well known, that trigonometric polynomials of the form $$P(t) = \sum^{N}_{n=-N}c_ne^{int}$$ are dense in $C(T)$, which is the set of all continuous, complex, $2\pi$ periodic functions.

Is it true, that trigonometric polynomials of the form $$P(t) = \sum^{N}_{n=-N}c_ne^{2\pi int}$$ are dense in the set of continuous, complex, $1$-periodic functions?