Repeat Problem 6.25 except using x 1 ( 0 ) = 0.25 x 1 ( 0 ) = 0.25 and x 2 ( 0 )

Repeat Problem 6.25 except using $x_1\left(0\right)=0.25$ and $x_2\left(0\right)=0$ radians as an initial guess.

Problem 6.25

The following nonlinear equations contain terms that are often found in the power flow equations:

$$\begin{array}{cc}& f_1\left(x\right)=10x_1\sin x_2+2=0\\ & f_2\left(x\right)=10{\left(x_1\right)}^2-10x_1\cos x_2+1=0\end{array}$$

Solve using the Newton-Raphson method starting with an initial guess of $x_1\left(0\right)=1$ and $x_2\left(0\right)=0$ radians and a stopping criteria of $\epsilon ={10}^{-4}$.