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1.5 Trigonometry

1.5 Trigonometry

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Question 201

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

1.5 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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