Express 13sin(x−α)\sqrt{13} \sin(x-\alpha)13sin(x−α) in the form asinx−bcosxa \sin x - b \cos xasinx−bcosx, where tanα=23\displaystyle \tan\alpha=\frac{2}{3}tanα=32 and 0≤α≤π2\displaystyle 0 \leq \alpha \leq \frac{\pi}{2}0≤α≤2π
Hence find the greatest value of (3sinx−2cosx)2(3 \sin x - 2 \cos x)^2(3sinx−2cosx)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,
3sinx−2cosx=1 3 \sin x - 2 \cos x = 1 3sinx−2cosx=1Give 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.