Radians

The deflection $D$ of a micro-cantilever, in micrometres, is modelled for small tilt angles $θ\theta$ (measured in radians) by the expression

\cos 4\theta + 3 \sin 2\theta - \tan 5\theta

Show that, for small values of $θ\theta$ , the deflection can be approximated by the quadratic form

Q\theta + R\theta^2

where $P$ , $Q$ and $R$ are constants to be found.

[4]

Use your answer to part (a) to find an approximation for the deflection when

\cos 0.16 + 3 \sin 0.08 - \tan 0.20

Give your answer to three decimal places.

[3]

Radians Questions

The deflection $D$ of a micro-cantilever, in micrometres, is modelled for small tilt angles $θ\theta$ (measured in radians) by the expression

\cos 4\theta + 3 \sin 2\theta - \tan 5\theta

Show that, for small values of $θ\theta$ , the deflection can be approximated by the quadratic form

Q\theta + R\theta^2

where $P$ , $Q$ and $R$ are constants to be found.

[4]

Use your answer to part (a) to find an approximation for the deflection when

\cos 0.16 + 3 \sin 0.08 - \tan 0.20

Give your answer to three decimal places.

[3]