A high-precision docking system in an aerospace facility uses two automated parallel assemblies, A A\,A and BBB, which oscillate vertically to dampen vibrations during a calibration cycle of 6π 6\pi\,6π minutes. At time t t\,t minutes after the cycle begins, the height hA h_A\,hA metres of assembly A A\,A above the hangar floor is given by hA=26.8−7sinth_A = 26.8 - 7\sin thA=26.8−7sint At time t t\,t minutes after the cycle begins, the height hB h_B\,hB metres of assembly B B\,B above the hangar floor is given by hB=7.4−5costh_B = 7.4 - 5\cos thB=7.4−5cost
Show that the initial vertical separation between assembly A A\,A and assembly B B\,B is 24.4 metres.
Show that the distance Δ \Delta\,Δ metres between the two assemblies at time t t\,t is given by Δ=19.4+Rcos(t+α)\Delta = 19.4 + R\cos(t + \alpha)Δ=19.4+Rcos(t+α) where R R\,R and α \alpha\,α are positive constants to be found. Give R R\,R in surd form and α \alpha\,α in radians to two decimal places.
Hence, determine the minimum vertical distance between the two assemblies. Give your answer to the nearest centimetre.
Practise Edexcel A Level Maths 7.4 Simplifying a cos x +- b sin x with exam-style questions for A Level Maths. 19 questions, 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.