Turn over 25 Question 11 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 11 is 6 marks) 26 12. In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) Solve, for 0 < θ  450°, the equation 5 cos 2 θ = 6 sin θ giving your answers to one decimal place. (5) (ii) (a) A student’s attempt to solve the question “ Solve, for –90° < x < 90°, the equation 3 tan x – 5 sin x = 0 ” is set out below. 3 tan x – 5 sin x = 0 3 sin cos x x – 5 sin x = 0 3 sin x – 5 sin x cos x = 0 3 – 5 cos x = 0 cos x = 3 5 x = 53.1° Identify two errors or omissions made by this student, giving a brief explanation of each. (2) The first four positive solutions, in order of size, of the equation cos (5α + 40°) = 3 5 are α1 , α2 , α3 and α4 (b) Find, to the nearest degree, the value of α4 (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________