How do I Solve for the unknowns phi and s using the newton-raphson method?

How do I solve these nonlinear equations for the unknowns using matlab? The angle phi and s using the newton-raphson method?

R sin (theta ) + L sin(phi) = H ....(1)

R cos(theta) + L cos(phi) =s....(2)

I know that

phi = arcsin ([H cos(theta) - s sin(theta)] /L) + theta

and

s =R cos(theta) + L cos(phi)s =R cos(theta) + L cos(phi)

Answer 1

[Roger Stafford]

How about solving first for phi in the first equation and then solving for s in the second equation in terms of this phi?

 t = asin((H-R*sin(theta))/L);

 phi = asin(t)

or

 phi = sign(t)*pi - t;

Then

 s = R*cos(theta) + L cos(phi);

This gives you two solutions for phi in the range -pi <= phi <= pi. There are of course infinitely many other solutions for phi in other 2*pi-length intervals.

You don't need to use newton-raphson.

[Mireya]

professor is requesting we use newton-raphson.

[Roger Stafford]

 http://en.wikipedia.org/wiki/Newton's_method#Nonlinear_systems_of_equations