Review question

# Where are the stationary points on $\cot x-8\cos x$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6549

## Suggestion

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.