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Radians

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Question 34

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

S(ϕ)=4cos⁡3ϕ−5sin⁡2ϕ+3tan⁡4ϕ S(\phi) = 4 \cos 3\phi - 5 \sin 2\phi + 3 \tan 4\phi S(ϕ)=4cos3ϕ−5sin2ϕ+3tan4ϕ
a.

Show that, for small values of ϕ\phiϕ,

S(ϕ)≈A+Bϕ+Cϕ2 S(\phi) \approx A + B\phi + C\phi^2 S(ϕ)≈A+Bϕ+Cϕ2

where A,BA, BA,B and CCC are constants to be found.

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b.

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

4cos⁡0.21−5sin⁡0.14+3tan⁡0.28 4 \cos 0.21 - 5 \sin 0.14 + 3 \tan 0.28 4cos0.21−5sin0.14+3tan0.28

Give your answer to three decimal places.

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Radians Questions

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