Year 2 Pure Chapter 6: Trigonometry Functions - Exam Questions (Total Marks 41)
1.	(a)	Prove that
sec2x – cosec2 x ≡ tan2x – cot2x.
(3)
(b)	Solve, for 0 < θ < 180°, the equation
	2cot2θ = 7cosecθ - 8,
	giving your answers to 1 decimal place.
(6)
 (Total 9 marks)

 

2.	(a)	Given that sin2θ + cos2θ ≡ 1, show that 1 + cot2θ ≡ cosec2θ.
(2)
 (b)	Solve, for 0 ≤ θ < 180°, the equation
	2cot2θ – 9cosecθ = 3,
	giving your answers to 1 decimal place.
(6)
(Total 8 marks)

3.	(a)	Given that sin2q + cos2q º 1, show that 1 + tan2q º sec2q.
(2)
(b)	Solve, for 0 £ q < 360°, the equation
2 tan2q + secq  = 1,
	giving your answers to 1 decimal place.
(6)
(Total 8 marks)

4.	(a)	Using sin2θ + cos2θ ≡ 1, show that cosec2θ – cot2 θ ≡ 1.
(2)
 (b)	Hence, or otherwise, prove that
cosec4θ – cot4θ ≡ cosec2θ + cot2θ.
(2)
(c)	Solve, for 90° < θ < 180°,
cosec4θ – cot4θ = 2 – cot θ.
(6)
(Total 10 marks)

	

5.
a) Sketch the graph of y = arcsin x					 (2 marks)
b) Sketch the graph of y = arccos x					 (2 marks)
c) Sketch the graph of y = arctan x					 (2 marks)