9.7 Parametric Differentiation

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A high-precision cam profile in a mechanical sensor follows a path defined by the equation

$\sin 4\theta \quad 0 \le x \le 6, \quad 0 \le \theta \le \frac{\pi}{8}$

where $x$ is the horizontal displacement in millimetres and $θ\theta$ is the angular position of the cam in radians.

Find $dxdθ\frac{dx}{d\theta}$ in terms of $θ\theta$ .

[2]

Hence show that

$dθdx=k36−x2\frac{d\theta}{dx} = \frac{k}{\sqrt{36-x^2}}$

where $k$ is a constant to be determined.

[3]

A specific calibration point $P (a, b)$ lies on the profile. At this point:

The rate of change of the angular position with respect to displacement, $dθdx\frac{d\theta}{dx}$ , is exactly $1123\frac{1}{12\sqrt{3}}$ .
Both $a$ and $b$ are positive constants.

Determine 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.