that varies, θ (b) find the minimum value of (2) V. that Kate’s speed has the value found in part (b), (c) find the distance (3) AB. Given instead that Kate’s speed is 1.68 m s–1, (d) find the two possible values of the angle given that 0 < < 150°. (6) θ, θ [June 2013 (Withdrawn) Q8] 8. [June 2013 (R) Q3] 9. f(x) = 7cos + sin x x Given that f(x) = where R > 0 and 0 < < 90°, Rcos(x a), a – (a) find the exact value of and the value of to one decimal place. (3) R a (b) solve the equation 7cos + sin = 5 x x for 0 < 360°, giving your answers to one decimal place. (5) x ≤ (c) State the values of for which the equation k 7cos + sin = x x k has only one solution in the interval 0 < 360°. (2) ≤ x [Jan 2013 Q4] 10. (a) Express 6 cos + 8 sin in the form cos ( where > 0 and 0 < R R – α), < . α Give the value of to 3 decimal places. (4) α (b) p( ) = , 0 2. Calculate (i) the maximum of p( ), (ii) the value of at which the maximum occurs. (4) [June 2012 Q8] 11. f(x) = 7 cos 2x 24 sin 2x. − Given that f(x) = cos (2x + where > 0 and 0 < < 90, R R α), α (a) find the value of and the value of (3) R α. (b) solve the equation 7 cos 2x 24 sin 2x = 12.5 − for 0 < 180, giving your answers to 1 decimal place. (5) x (c) Express 14 cos2 48 sin cos in the form cos 2x + sin 2x + where and x x x a b c, a, b, c − are constants to be found. (2) (d) using your answers to parts (a) and (c), deduce the maximum value of
that θ varies, (b) find the minimum value of V. (2) that Kate’s speed has the value found in part (b), (c) find the distance AB. (3) Given instead that Kate’s speed is 1.68 m s–1, (d) find the two possible values of the angle θ, given that 0 < θ < 150°. (6) [June 2013 (Withdrawn) Q8] 8. [June 2013 (R) Q3] 9. f(x) = 7cos x + sin x Given that f(x) = Rcos(x – a), where R > 0 and 0 < a < 90°, (a) find the exact value of R and the value of a to one decimal place. (3) (b) solve the equation 7cos x + sin x = 5 for 0 ≤ x < 360°, giving your answers to one decimal place. (5) (c) State the values of k for which the equation 7cos x + sin x = k has only one solution in the interval 0 ≤ x < 360°. (2) [Jan 2013 Q4] 10. (a) Express 6 cos + 8 sin in the form R cos ( – α), where R > 0 and 0 < α < . Give the value of α to 3 decimal places. (4) (b) p( ) = , 0 2. Calculate (i) the maximum of p( ), (ii) the value of at which the maximum occurs. (4) [June 2012 Q8] 11. f(x) = 7 cos 2x − 24 sin 2x. Given that f(x) = R cos (2x + α), where R > 0 and 0 < α < 90, (a) find the value of R and the value of α. (3) (b) solve the equation 7 cos 2x − 24 sin 2x = 12.5 for 0 x < 180, giving your answers to 1 decimal place. (5) (c) Express 14 cos2 x − 48 sin x cos x in the form a cos 2x + b sin 2x + c, where a, b, and c are constants to be found. (2) (d) using your answers to parts (a) and (c), deduce the maximum value of
C3-Chp7-TrigExamQuestions.docx