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.
317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.