Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

For a curve, the parametric equations are $x = 3\sin 2t$ and $y = \tan t + \cot t$, with $0 < t < \tfrac{1}{2}\pi$.
(a)[5]

Show that the derivative satisfies $\frac{dy}{dx} = -\frac{2}{3\sin^2 2t}$.

(b)[3]

Find the equation of the normal to the curve at the point for which $t = \frac{1}{4}\pi$. Write your answer in the form $py + qx + r = 0$, where $p$, $q$ and $r$ are integers.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate to find $\tfrac{dx}{dt}=6\cos2t$.

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