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.)
221 exam-style questions on CCEA A Level Maths 3.4 Trigonometry (A-level only), covering 3.4.1 Trigonometry (A-level only), 3.4.2 Trigonometry (A-level only), 3.4.3 Trigonometry (A-level only), 3.4.4 Trigonometry (A-level only), 3.4.5 Trigonometry (A-level only), 3.4.6 Trigonometry (A-level only), 3.4.7 Trigonometry (A-level only), and 3.4.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.