1. Show that the roots of $\sin (x)$ may be approximated by the Newton-Raphson formula

1. Use this formula, with a starting value of $x_0=3,$ to show that

Notice that $\sin (\pi )=0$ so that $\pi$ is a root of $\sin (x)=0$. We know that $\pi \approx 3$ so this is a good starting value for $x_0$.

Give your second approximation, $x_2$, to $9$ decimal places.