(i) The graph of \(y = 3 \sin x\) is a sine wave with amplitude 3, oscillating between -3 and 3, over the interval \(-\pi \leq x \leq \pi\). The maximum point is at \(x = \frac{\pi}{2}\), where \(y = 3\).

(ii) The line \(y = kx\) passes through the maximum point \(\left( \frac{\pi}{2}, 3 \right)\). Substituting into the line equation gives:

\(3 = k \left( \frac{\pi}{2} \right)\)

Solving for \(k\):

\(k = \frac{6}{\pi}\)

(iii) To find the other intersection point, set \(y = 3 \sin x = kx\) and solve for \(x\):

\(3 \sin x = \frac{6}{\pi} x\)

At \(x = -\frac{\pi}{2}\), \(\sin x = -1\), so:

\(3(-1) = \frac{6}{\pi} \left(-\frac{\pi}{2}\right)\)

\(-3 = -3\)

Thus, the coordinates are \(\left( -\frac{\pi}{2}, -3 \right)\).