C3 Chapter 7 Trigonometry Exam Questions – – Section A Provey/Solvey Questions – [Jan 2014 (I) Q7] (a) that (You may use the double angle formulae and the identity ) (4) (b) Hence solve the equation giving answers in the interval . Solutions based entirely on graphical or numerical methods are not acceptable.(6) (ii) Given that and that , show that , 0 < < 1 x (3) [June 2013 Q3] 2. Given that 2 cos (x + 50)° = sin (x + 40)°. (a) Show, without using a calculator, that tan = tan 40°. x° (4) (b) Hence solve, for 0 < 360, ≤ θ 2 cos (2θ + 50)° = sin (2θ + 40)°, giving your answers to 1 decimal place. (4) [June 2013 (R) Q6] 3. (i) Use an appropriate double angle formula to show that cosec 2x = cosec sec x x, λ and state the value of the constant (3) λ. (ii) Solve, for 0 < 2π, the equation ≤ θ 3sec2 + 3 sec = 2 tan2 θ θ θ You must show all your working. Give your answers in terms of (6) π. (i) Without using a calculator, find the exact value of [Jan 2013 Q6] 4. (sin 22.5° + cos 22.5°)2. You must show each stage of your working. (5) (ii) (a) Show that cos 2 + sin = 1 may be written in the form sin2 sin = 0, stating the value of k k. – (2) (b) Hence solve, for 0 < 360°, the equation cos 2 + sin = 1. (4) [June 2012 Q5] 5. (a) Express 4 cosec2 2θ cosec2 in terms of sin and cos (2) − θ θ θ. (b) Hence show that 4 cosec2 2θ cosec2 = sec2 . − θ θ (4)
C3 – Chapter 7 Trigonometry – Exam Questions Section A – Provey/Solvey Questions [Jan 2014 (I) Q7] (a) that (You may use the double angle formulae and the identity ) (4) (b) Hence solve the equation giving answers in the interval . Solutions based entirely on graphical or numerical methods are not acceptable.(6) (ii) Given that and that , show that , 0 < x < 1 (3) [June 2013 Q3] 2. Given that 2 cos (x + 50)° = sin (x + 40)°. (a) Show, without using a calculator, that tan x° = tan 40°. (4) (b) Hence solve, for 0 ≤ θ < 360, 2 cos (2θ + 50)° = sin (2θ + 40)°, giving your answers to 1 decimal place. (4) [June 2013 (R) Q6] 3. (i) Use an appropriate double angle formula to show that cosec 2x = λ cosec x sec x, and state the value of the constant λ. (3) (ii) Solve, for 0 ≤ θ < 2π, the equation 3sec2 θ + 3 sec θ = 2 tan2 θ You must show all your working. Give your answers in terms of π. (6) [Jan 2013 Q6] 4. (i) Without using a calculator, find the exact value of (sin 22.5° + cos 22.5°)2. You must show each stage of your working. (5) (ii) (a) Show that cos 2 + sin = 1 may be written in the form k sin2 – sin = 0, stating the value of k. (2) (b) Hence solve, for 0 < 360°, the equation cos 2 + sin = 1. (4) [June 2012 Q5] 5. (a) Express 4 cosec2 2θ − cosec2 θ in terms of sin θ and cos θ. (2) (b) Hence show that 4 cosec2 2θ − cosec2 θ = sec2 θ . (4)
C3-Chp7-TrigExamQuestions.docx