The displacement x(t)x(t)x(t) of a physical structure subjected to harmonic wind loading is modelled by the function x(t)=20cos(ωt)+21sin(ωt)x(t) = 20 \cos(\omega t) + 21 \sin(\omega t)x(t)=20cos(ωt)+21sin(ωt).
Given that
20cos(ωt)+21sin(ωt)≡Rcos(ωt−α) 20 \cos(\omega t) + 21 \sin(\omega t) \equiv R \cos(\omega t - \alpha) 20cos(ωt)+21sin(ωt)≡Rcos(ωt−α)find the value of RRR, representing the maximum displacement of the structure, where R>0R > 0R>0.
Circle the correct answer from the options below:
212121 \qquad 292929 \qquad 414141 \qquad 841841841
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 110 questions covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions, 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.
