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1.5 Trigonometry

1.5 Trigonometry

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Question 173

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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Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

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