(a)[4]
Show that $\frac{dy}{dx} = 6\cos^5\theta - 5\cos^3\theta$.
(b)[5]
Find the equation of the normal to the curve at the point where it meets the $x$-axis. Give your answer in the form $y = mx + c$, where $m$ and $c$ are exact constants.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is described by the parametric equations $x = \tan \theta$, $y = \sin \theta - 2\sin^3 \theta$, for $0 < \theta < \frac{1}{2}\pi$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try to use the chain rule when differentiating $y$, or when simplifying $y$, together with the product rule” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI