(i)[4]
Show that the result is $\frac{dy}{dx} = \frac{8\cos \theta}{1 - 4\cos \theta}$.
(ii)[4]
Find the coordinates of the point on the curve for which the gradient is $-4$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
A curve has parametric equations $x = \cos 2\theta - \cos \theta$, $y = 4\sin^2 \theta$, for $0 \leq \theta \leq \pi$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State $\frac{dx}{d\theta}=-2\sin 2\theta+\sin\theta$ or, alternatively, $\frac{dy}{d\theta}=8\sin\theta\cos\theta$” …
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