5.5 Small Angle Approximations

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A micro-electromechanical sensor records a signal $S$ as a function of its angular displacement $ϕ\phi$ (measured in radians). The response function is given by

$S(ϕ)=4cos⁡3ϕ−5sin⁡2ϕ+3tan⁡4ϕS(\phi) = 4 \cos 3\phi - 5 \sin 2\phi + 3 \tan 4\phi$

Show that, for small values of $ϕ\phi$ ,

$S(ϕ)≈A+Bϕ+Cϕ2S(\phi) \approx A + B\phi + C\phi^2$

where $A, B$ and $C$ are constants to be found.

[4]

Use your answer to part (a) to determine an approximation for

$\cos 0.21 - 5 \sin 0.14 + 3 \tan 0.28$

Give your answer to three decimal places.

[4]

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.