Express 5sinx+12cosx5\sin x + 12\cos x5sinx+12cosx 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°0°≤α≤90°. Give α \alpha\,α to one decimal place.
Hence find the maximum value of 5sinx+12cosx5\sin x + 12\cos x5sinx+12cosx, and the smallest positive value of x x\,x at which this maximum occurs.
225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.