The lateral displacement, xxx mm, of a high-precision vibrating needle is modeled by the equation
x=14cos2(4y)0<y<π8x = 14 \cos^2(4y) \qquad 0 < y < \frac{\pi}{8}x=14cos2(4y)0<y<8π
where yyy is the angle of the driving cam in radians.
Show that the rate of change of the cam angle with respect to displacement is given by
dydx=−1ABx−x2\frac{dy}{dx} = -\frac{1}{A\sqrt{Bx - x^2}}dxdy=−ABx−x21
where AAA and BBB are integers to be found.
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.