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FP1 – Chapter 5 Exam Questions 1. Solve the equation cos x 0.5, 6 in the interval 0 < x < 2π, leaving your answers in terms of π. (6) (Total 6 marks) 2. The angle x radians satisfies the equation cos (2x + (a) 1 )= 6 2 Find the general solution of this equation, giving the roots as exact values in terms of π. (6) (b) Find the number of roots of the equation which lie between 0 and 2 π. (2) (Total 8 marks) 3. (a) 3 Write down the values of tan and tan . 4 4 (2) (b) It is given that x satisfies the equation 2 sin2 x + sin x cos x = cos2x. (i) By dividing both sides of this equation by cos2 x, show that 2 tan2 x + tan x 1 = 0. (2) (ii) Solve this quadratic equation for tan x. (2) (iii) Hence find all possible values of x in the interval 0 < x < π. Give each answer to three significant figures. (2) (Total 8 marks) South Wolds Comprehensive School 1