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1.8 E: Trigonometry

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Question 105

The displacement of a buoy from its equilibrium position, in decimetres, is modeled by the function

h(t)=12cos⁡t−5sin⁡t h(t) = 12\cos t - 5\sin t h(t)=12cost−5sint

where ttt is the time in minutes since the start of the observation.

a.

Express h(t)h(t)h(t) in the form Rcos⁡(t+α)R\cos(t + \alpha)Rcos(t+α), where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of RRR and the value of α\alphaα, in radians, to 3 decimal places.

[3]
b.

Let the stability index of the buoy be defined by S(t)=10−3h(4t)S(t) = 10 - 3h(4t)S(t)=10−3h(4t).

Using the answer to part (a), (i) write down the exact maximum value of S(t)S(t)S(t). (ii) find the smallest positive value of ttt for which this maximum value occurs, giving your answer to 2 decimal places.

[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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