9.7 Parametric Differentiation

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The movement of a precision robotic arm across a flat surface is defined by the parametric relationship

$\cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4}$

where $x$ is the horizontal position in millimetres and $y$ is the control angle in radians.

Find $dxdy\frac{dx}{dy}$ in terms of $y$ .

[2]

Hence show that

$dydx=k36−x2\frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}}$

where $k$ is a constant to be found.

[3]

A specific calibration point $P (a, b)$ lies on the path of the arm. Given that

the gradient of the path at $P$ is $−16-\frac{1}{6}$
both $a$ and $b$ are positive constants

find the exact values of $a$ and $b$ .

[4]

9.7 Parametric Differentiation Questions

Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.