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1.5 Trigonometry

1.5 Trigonometry

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Question 189

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]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

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.

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