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1.8 E: Trigonometry

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Question 187

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=26.8−7sin⁡t h_A = 26.8 - 7\sin t hA​=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=7.4−5cos⁡t h_B = 7.4 - 5\cos t hB​=7.4−5cost
a.

Show that the initial vertical separation between assembly A A\,A and assembly B B\,B is 24.4 metres.

[3]
b.

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.

[4]
c.

Hence, determine the minimum vertical distance between the two assemblies. Give your answer to the nearest centimetre.

[3]

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) 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.

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