Given that R=26R = \sqrt{26}R=26 and tanα=15\displaystyle \tan \alpha = \frac{1}{5}tanα=51, where R>0 R > 0\,R>0 and 0≤α≤π2\displaystyle 0 \leq \alpha \leq \frac{\pi}{2}0≤α≤2π
Show that
f(x)=5cosθ+sinθ f(x) = 5 \cos \theta + \sin \theta f(x)=5cosθ+sinθHence, solve for 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π, the equation
5cosθ+sinθ=2 5 \cos \theta + \sin \theta = 2 5cosθ+sinθ=2Give your answers to 2 decimal places.
Calculate the minimum value of
5cos4x+sin4x+15 5 \cos 4x + \sin 4x + 15 5cos4x+sin4x+15Find the smallest positive value of x x\,x for which this minimum occurs.
Give your answer 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.