It is given that
f(x)=3cosx−4sinxf(x) = 3\cos x - 4\sin xf(x)=3cosx−4sinx
and that f(x)=Rcos(x+α)f(x) = R\cos(x + \alpha)f(x)=Rcos(x+α), where R>0 R > 0\,R>0 and 0°≤α≤90°0° \leq \alpha \leq 90°0°≤α≤90°.
Find the value of R R\,R and the value of α\alphaα, giving α \alpha\,α to one decimal place.
Hence solve, for 0°≤x≤360°0° \leq x \leq 360°0°≤x≤360°, the equation
3cosx−4sinx=13\cos x - 4\sin x = 13cosx−4sinx=1
Give your answers to one decimal place.
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.