(i) To find the \(x\)-coordinate of the minimum point \(M\), we need to find the derivative of \(y = \frac{\sin x}{x}\) and set it to zero.

Using the quotient rule, the derivative is:

\(y' = \frac{x \cos x - \sin x}{x^2}\).

Setting \(y' = 0\), we have:

\(x \cos x - \sin x = 0\).

Rearranging gives:

\(x \cos x = \sin x\).

Dividing both sides by \(\cos x\), we get:

\(x = \tan x\).

(ii) Using the iterative formula \(x_{n+1} = \arctan(x_n) + \pi\), we start with an initial guess and iterate:

1. \(x_1 = \arctan(x_0) + \pi\)

2. \(x_2 = \arctan(x_1) + \pi\)

Continue iterating until the value stabilizes to 4 decimal places.

The final \(x\)-coordinate of \(M\) is 4.49, correct to 2 decimal places.