Hello : I have a problem whit this exercise

Decide which of the following are subrings of the ring of all functions from the closed interval [0,1] to $\displaystyle \mathbb{R}$:

1)the set of all rational linear combinations of the functions sin (nx) and cos (x) where m, n

$\displaystyle \in{} $ {0,1,2,...}

2)the set of all polynomial functions

3)the set of all functions that have an infinite number of zeros

2 is a subring but not 1 and 3, but I can not establish the conclusion good, I hope some help

Thanks