1. a) Express 2cos x - sin x in the form Rcos (x + a), where R is a positive constant and α is an angle between 0° and 360°. b) Given that 0 ≤ x < 360° (i) solve 2cos x - sin x = 1 (ii) deduce the solution set of the inequality 2cos x- sin x ≥ 1. (Marks available: 6) Answer Answer outline and marking scheme for question: 1 Give yourself marks for mentioning any of the points below: a) Using the Rcos formula give: and Therefore (2 marks) b) (i) input values into the Rcos formula solving the above equation gives x = 36.9o and x = 270o. (2 marks) (ii) solving the given in-equality gives: (2 marks) (Marks available: 6) 2. The diagram shows the triangle ABC in which AB = 7 cm, BC = 9cm and CA = 8cm. a) Use the cosine rule to find cos C, giving your answer as a fraction in its lowest terms. b) Hence show that sin C = c) Find sinA in the form where p and q are positive integers to be determined. (Marks available: 7) Answer Answer outline and marking scheme for question: 2 Give yourself marks for mentioning any of the points below: a) Applying the cosine rule gives: (2 marks) b) Rearranging gives: (2 marks) c) Appling the sine rule gives: (3 marks) Total 7 marks 3. a) Express 2 sin θ cos 6θ as a difference of two sines. b) Hence prove the identity c) Deduce that (Marks available: 7) Answer Answer outline and marking scheme for question: 3 Give yourself marks for mentioning any of the points below: a) Using the sine rule: 2sin θ cost 6θ = sin 7θ - sin 5θ (1 mark) b) Applying the sine rule again: 2sin θ cost 4θ = sin 5θ - sin 3θ 2sin θ cos 2θ = sin 3θ - sin θ Adding the three expressions above, gives: (3 marks) c) Substitute θ = 2π/7. Putting this into the equation in (b) gives: . (3 marks) (Marks available: 7)