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.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.