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1.8 E: Trigonometry

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Question 153

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

D=2cos⁡4θ+3sin⁡2θ−tan⁡5θ D = 2 \cos 4\theta + 3 \sin 2\theta - \tan 5\theta D=2cos4θ+3sin2θ−tan5θ
a.

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

P+Qθ+Rθ2 P + Q\theta + R\theta^2 P+Qθ+Rθ2

where PPP, QQQ and RRR are constants to be found.

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b.

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

2cos⁡0.16+3sin⁡0.08−tan⁡0.20 2 \cos 0.16 + 3 \sin 0.08 - \tan 0.20 2cos0.16+3sin0.08−tan0.20

Give your answer to three decimal places.

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Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

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