The deflection DDD of a micro-cantilever, in micrometres, is modelled for small tilt angles θ\thetaθ (measured in radians) by the expression
D=2cos4θ+3sin2θ−tan5θ D = 2 \cos 4\theta + 3 \sin 2\theta - \tan 5\theta D=2cos4θ+3sin2θ−tan5θShow 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+Rθ2where PPP, QQQ and RRR are constants to be found.
Use your answer to part (a) to find an approximation for the deflection when
2cos0.16+3sin0.08−tan0.20 2 \cos 0.16 + 3 \sin 0.08 - \tan 0.20 2cos0.16+3sin0.08−tan0.20Give your answer to three decimal places.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) 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.
