4
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The diagram shows the curve \(y = \frac { \sin x } { x }\) for \(0 < x \leqslant 2 \pi\), and its minimum point \(M\).
- Show that the \(x\)-coordinate of \(M\) satisfies the equation
$$x = \tan x$$
- The iterative formula
$$x _ { n + 1 } = \tan ^ { - 1 } \left( x _ { n } \right) + \pi$$
can be used to determine the \(x\)-coordinate of \(M\). Use this formula to determine the \(x\)-coordinate of \(M\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.