Sketch the graph of the curve \(y = 3 \sin x\), for \(- \pi \leqslant x \leqslant \pi\).
The straight line \(y = k x\), where \(k\) is a constant, passes through the maximum point of this curve for \(- \pi \leqslant x \leqslant \pi\).
Find the value of \(k\) in terms of \(\pi\).
State the coordinates of the other point, apart from the origin, where the line and the curve intersect.