The lateral displacement, xxx mm, of a high-precision vibrating needle is modeled by the equation
x=14cos2(4y)0<y<π8 x = 14 \cos^2(4y) \qquad 0 < y < \frac{\pi}{8} x=14cos2(4y)0<y<8πwhere 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−x21where AAA and BBB are integers to be found.
35 exam-style questions on Edexcel A Level Maths 9.7 Parametric Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.