Show that the equation
4cosα+1=3sinαtanα 4\cos \alpha + 1 = 3 \sin \alpha \tan \alpha 4cosα+1=3sinαtanαcan be written in the form
7cos2α+cosα−3=0 7\cos^2 \alpha + \cos \alpha - 3 = 0 7cos2α+cosα−3=0A light-sensitive robotic arm measures the angle ϕ\phiϕ (in radians) of incoming radiation. The arm reaches a steady state when ϕ\phiϕ satisfies:
4cos3ϕ+1=3sin3ϕtan3ϕ 4\cos 3\phi + 1 = 3 \sin 3\phi \tan 3\phi 4cos3ϕ+1=3sin3ϕtan3ϕDetermine all possible values for ϕ\phiϕ in the interval 0≤ϕ<2π30 \le \phi < \frac{2\pi}{3}0≤ϕ<32π, 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.
