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.
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.