5.5 Small Angle Approximations

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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]

5.5 Small Angle Approximations Questions

Practise Edexcel A Level Maths 5.5 Small Angle Approximations with exam-style questions for A Level Maths. 25 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.