A robotic arm's horizontal extension EEE (in cm) is modelled by the function E(α)=5cos2α+14cosαE(\alpha) = 5 \cos 2\alpha + 14 \cos \alphaE(α)=5cos2α+14cosα, where α \alpha\,α is the motor angle in degrees and 0≤α<360∘0 \le \alpha < 360^\circ0≤α<360∘. Determine, to one decimal place, the values of α \alpha\,α for which the extension is exactly 3 cm. (Solutions based entirely on graphical or numerical methods are not acceptable.)
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.