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1.8 E: Trigonometry

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Question 201

An offshore wave-energy converter consists of a floating buoy and a submerged dampener plate that both move vertically due to ocean swells. Over a specific operating cycle, the height hB h_B\,hB​ metres of the buoy above the seabed at time t t\,t seconds is given by

hB=50−7sin⁡t h_B = 50 - 7\sin t hB​=50−7sint

The height hD h_D\,hD​ metres of the dampener plate above the seabed at time t t\,t seconds is given by

hD=15−4cos⁡t h_D = 15 - 4\cos t hD​=15−4cost
a.

Show that the initial vertical distance between the buoy and the dampener plate is 39 metres.

[2]
b.

Show that the distance d d\,d metres between the buoy and the dampener plate at time t t\,t is given by

d=35+Rcos⁡(t+α) d = 35 + R\cos(t + \alpha) d=35+Rcos(t+α)

where R R\,R and α \alpha\,α are positive constants to be found. Give α \alpha\,α in radians to two decimal places.

[4]
c.

Hence, find the minimum distance between the buoy and the dampener plate. Give your answer to the nearest centimetre.

[2]

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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