Functions f:N→R, g:N→R are such that

f(n+1)=f(n)cos(g(n))−g(n)sin(g(n))
g(n+1)=f(n)sin(g(n))+g(n)cos(g(n))

​ If f(1)=0.8 and g(1)=0.6, find the limit of f(n) as n tends towards infinity.