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1.5 Trigonometry

1.5 Trigonometry

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Question 205

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]
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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