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 (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.