A mechanical engineer models the efficiency, EEE, of a specialized turbine using the function
E(θ)=4cos2θ+2cosθ+6 E(\theta) = 4 \cos 2\theta + 2 \cos \theta + 6 E(θ)=4cos2θ+2cosθ+6where 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.)
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.
