(i)[3]
Show that $\frac{dy}{dx} = -3\sin t\cos t$.
(ii)[2]
Find the gradient of the curve at the origin.
(iii)[4]
Find the values of $t$ for which the curve has gradient 1, giving your answers correct to 2 significant figures.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The diagram depicts the curve defined by the parametric equations $x = \sin t + \cos t$, $y = \sin^3 t + \cos^3 t$, for $\frac{\pi}{4} < t < \frac{5\pi}{4}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $y$ to give $3\sin^2 t\cos t-3\cos^2 t\sin t$” …
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