Consider the nonlinear system

cos(x) = 2 sin(y)

x^2+y^2= 1

a) Use Newton's method to find a solution to this system. Output the entries of your solution and the residual (if you are solving 0 =F(x), the residual of x is F(x)

and should be close to zero).

b) It turns out this problem has exactly two solutions. Find both.