Express 2sinx−3cosx2\sin x - 3\cos x2sinx−3cosx in the form Rsin(x−α)R\sin(x - \alpha)Rsin(x−α), where R>0 R > 0\,R>0 and 0≤α≤π2\displaystyle 0 \leq \alpha \leq \frac{\pi}{2}0≤α≤2π. Give R R\,R in surd form and α \alpha\,α to three decimal places.
Hence find the greatest value of (2sinx−3cosx)2(2\sin x - 3\cos x)^2(2sinx−3cosx)2, and the smallest positive value of x x\,x at which this greatest value occurs.
Solve, for 0≤x≤2π0 \leq x \leq 2\pi0≤x≤2π, the equation
2sinx−3cosx=12\sin x - 3\cos x = 12sinx−3cosx=1
Give your answers to three 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.