The torque τ \tau\,τ in a precision galvanometer is given by the interaction of two magnetic fields. For the system to be in equilibrium at an angle α\alphaα, the following condition must be met:
5cosα+3=4sinαtanα 5\cos \alpha + 3 = 4\sin \alpha \tan \alpha 5cosα+3=4sinαtanαShow that this condition can be rewritten as the quadratic equation
9cos2α+3cosα−4=0 9\cos^2 \alpha + 3\cos \alpha - 4 = 0 9cos2α+3cosα−4=0A specific test run observes the system over the time interval 0≤t<π0 \le t < \pi0≤t<π, where the angle is driven such that α=2t\alpha = 2tα=2t. Determine the times t t\,t at which 5cos(2t)+3=4sin(2t)tan(2t)5\cos(2t) + 3 = 4\sin(2t) \tan(2t)5cos(2t)+3=4sin(2t)tan(2t), 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.
