The equation of a curve is \[ y = \cot x - 8 \cos x, \quad (0 < x < \pi). \] Find the coordinates of the points on the curve where \(\dfrac{dy}{dx} = 0\).

Should we include \(\dfrac{\pi}{2}\) in the domain of this function?

If we think of \(\cot x\) as \(\dfrac{1}{\tan x}\), then as \(\tan \dfrac{\pi}{2}\) is not defined, neither is \(\cot x\) at this value.

But what if we define \(\cot x=\dfrac{\cos x}{\sin x}\) instead?

Sketch the curve.

As well as the stationary points, we should consider the \(x\)-intercepts and any asymptotes.