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.)
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.