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
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.