3.5.4 Differentiation (A-level only)

The lateral displacement, $x$ mm, of a high-precision vibrating needle is modeled by the equation

\cos^2(4y) \qquad 0 < y < \frac{\pi}{8}

where $y$ 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

\frac{dy}{dx} = -\frac{1}{A\sqrt{Bx - x^2}}

where $A$ and $B$ are integers to be found.

[6]

3.5.4 Differentiation (A-level only) Questions

The lateral displacement, $x$ mm, of a high-precision vibrating needle is modeled by the equation

\cos^2(4y) \qquad 0 < y < \frac{\pi}{8}

where $y$ 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

\frac{dy}{dx} = -\frac{1}{A\sqrt{Bx - x^2}}

where $A$ and $B$ are integers to be found.

[6]