Newton method - example for setup

I need help setting up this question. I am not sure how to determine the incrementation for linear equations solving nonlinear equations. This is the question:

Construct a system of 4 nonlinear equations using the combination of sin(xi), cos(xi), xi^2, xi^3, exp(xi) for i=1,2,3,4.

It should look like this in equation form:

f1(x)=sin(x1)+2*x2^2-x3*x4^2+x4=0

Then I have to solve it with Newton method.It requires me to solve the system of linar equations for each increment by writing a subroutine to solve them using LU decomposition with privoting plus forward and backward scheme. It calls the subroutine of the linear systems to move forward.

It gives a hint of setting Nmax=20 to avoid getting a deadloop and suggests using 4-6 iterations starting with a system of two, them 3 and finally 4.