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−tan5θD = 2 \cos 4\theta + 3 \sin 2\theta - \tan 5\thetaD=2cos4θ+3sin2θ−tan5θ
Show that, for small values of θ\thetaθ, the deflection can be approximated by the quadratic form
P+Qθ+Rθ2P + Q\theta + R\theta^2P+Qθ+Rθ2
where 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−tan0.202 \cos 0.16 + 3 \sin 0.08 - \tan 0.202cos0.16+3sin0.08−tan0.20
Give your answer to three decimal places.
Practise Edexcel A Level Maths Radians with exam-style questions for A Level Maths. 52 questions covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations, matched to the Edexcel A Level Maths (9MA0) 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.