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≤π2\displaystyle 0 \leq \alpha \leq \frac{\pi}{2}0≤α≤2π
Hence find the greatest value of (5sinx−12cosx)2(5 \sin x - 12 \cos x)^2(5sinx−12cosx)2 and find, the smallest positive value of x x\,x for which this maximum occurs
Solve, for 0≤x≤2π0 \leq x \leq 2\pi0≤x≤2π,
5sinx−12cosx=5 5 \sin x - 12 \cos x = 5 5sinx−12cosx=5Give your answers to 3 decimal places.
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.