An automated tracking sensor for a wind turbine calculates its optimal inclination angle θ\thetaθ relative to the wind direction. For a specific range of wind speeds, the mechanical equilibrium of the sensor is maintained when
Show that the equation
6tanθ=cosθ 6 \tan \theta = \cos \theta 6tanθ=cosθmay be rewritten in the form
sin2θ+6sinθ−1=0 \sin^2 \theta + 6 \sin \theta - 1 = 0 sin2θ+6sinθ−1=0Hence solve, for 0∘≤x≤180∘0^\circ \le x \le 180^\circ0∘≤x≤180∘, the equation
6tan(2x+10∘)=cos(2x+10∘) 6 \tan (2x + 10^\circ) = \cos (2x + 10^\circ) 6tan(2x+10∘)=cos(2x+10∘)giving your answers to 2 decimal places.
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.
