Symmetry in DFT plot in MATLAB

%Code for DFT of a simple sine signal:

clc

clear all

close all

N=16;

n=0:N-1;

w=2*pi/N;

x=sin(w*n);

y=fft(x,N);

k=n;

subplot(2,1,1);

stem(k,abs(y));

subplot(2,1,2);

stem(k,angle(y));