Express 8sinx+15cosx8 \sin x + 15 \cos x8sinx+15cosx in the form Rsin(x+α)R \sin (x + \alpha)Rsin(x+α), where R>0 R > 0\,R>0 and 0≤α≤90∘0 \leq \alpha \leq 90^\circ0≤α≤90∘. Give your answer for α \alpha\,α to 1 decimal place.
Hence find the maximum value of 8sinx+15cosx8 \sin x + 15 \cos x8sinx+15cosx and find the smallest positive value of x x\,x for which this maximum occurs. Give your answer for x x\,x to 1 decimal place.
348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.