(a)[5]
Determine the value of $\theta$ at $P$; give your answer correct to $3$ significant figures.
(b)[6]
Determine the gradient of the curve at $Q$, and give your answer correct to $3$ significant figures.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is given parametrically by $x = 3\cos 2\theta$, $y = 4\sin\theta$, with $\pi \leq \theta \leq \dfrac{3\pi}{2}$. The points $P$ and $Q$ are on the curve. At $P$, the gradient of the curve is $2$. The line $3x + y = 0$ intersects the curve at $Q$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State $\frac{dx}{d\theta}=-6\sin2\theta$ together with $\frac{dy}{d\theta}=4\cos\theta$” …
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