(i)[3]
Obtain an expression for $\frac{dy}{dx}$ written in terms of $\theta$.
(ii)[4]
Hence determine the exact coordinates of the point on the curve where the tangent is parallel to the $y$-axis.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
A curve is given parametrically by $x = 2\sin\theta + \sin 2\theta$ and $y = 2\cos\theta + \cos 2\theta$, with $0 < \theta < \pi$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\dfrac{dx}{d\theta}=2\cos\theta+2\cos2\theta$ and $\dfrac{dy}{d\theta}=-2\sin\theta-2\sin2\theta$” …
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