(i) Start with the equation \(2 \cos x + 3 \sin x = 0\).

Rearrange to \(\tan x = -\frac{2}{3}\).

Find \(x\) using the inverse tangent function: \(x = 146.3^\circ\) or \(x = 326.3^\circ\).

(ii) Sketch the graphs of \(y = 2 \cos x\) and \(y = -3 \sin x\) over the interval \(0^\circ \leq x \leq 360^\circ\). The cosine graph starts at the top of the curve, while the sine graph is inverted and starts on the x-axis.

(iii) From the graphs, determine where \(2 \cos x + 3 \sin x > 0\). This occurs when \(x < 146.3^\circ\) and \(x > 326.3^\circ\).