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1.8 E: Trigonometry

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Question 162

A mechanical engineer models the efficiency, EEE, of a specialized turbine using the function

E(θ)=4cos⁡2θ+2cos⁡θ+6 E(\theta) = 4 \cos 2\theta + 2 \cos \theta + 6 E(θ)=4cos2θ+2cosθ+6

where θ \theta\,θ is the blade pitch angle in degrees.

Find all values of θ\thetaθ, for 0≤θ<360∘0 \le \theta < 360^\circ0≤θ<360∘, for which the efficiency is exactly 5. Give your solutions to one decimal place where appropriate.

(Solutions based entirely on graphical or numerical methods are not acceptable.)

[5]
Markscheme

1.8 E: Trigonometry Questions

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

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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