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.
84 exam-style questions on CCEA A Level Maths 1.4 Trigonometry, covering 1.4.1 Trigonometry, 1.4.2 Trigonometry, 1.4.3 Trigonometry, 1.4.4 Trigonometry, 1.4.5 Trigonometry, 1.4.6 Trigonometry, and 1.4 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.