We consider the problem of approximating and learning disjunctions (or equivalently, conjunctions) on symmetric distributions over {0; 1}n. Symmetric distributions are distributions whose PDF is invariant under any permutation of the variables. We prove that for every symmetric distribution D, there exists a set of nO(log (1/e)) functions S, such that for every disjunction c, there is function p, expressible as a linear combination of functions in S, such that p e-approximates c in l1 distance on D or Ex-D[|c(x) - p(x)|] ≤ e. This implies an agnostic learning algorithm for disjunctions on symmetric distributions that runs in time nO(log (1/e)). The best known previous bound is nO(1/e4) and follows from approximation of the more general class of halfspaces (Wimmer, 2010). We also show that there exists a symmetric distribution D, such that the minimum degree of a polynomial that 1/3-approximates the disjunction of all n variables in l1 distance on D is Ω(√n). Therefore the learning result above cannot be achieved via l1-regression with a polynomial basis used in most other agnostic learning algorithms. Our technique also gives a simple proof that for any product distribution D and every disjunction c, there exists a polynomial p of degree O(log (1/e)) such that p e-approximates c in l1 distance on D. This was first proved by Blais et al. (2008) via a more involved argument.