2.2 Chapter review π π ) = 1 for 0 ⩽ x ⩽ 3 4
1
Solve 2cos2 (3x −
2
Show that (sec2 θ −1) + (cosec2 θ −1) = sec θ ⋅ cossec θ
3
y
(4 marks) (5 marks)
5 4 3 2 1 0
0
p 2
p
3p 2
2p
x
The graph shows the graph of y = a + bsincx Find the value of a, b and c 4
Solve the following equations (i) 4sin2x + 5cos2x = 0
5
(3 marks)
0° ⩽ x ⩽ 180°
0° ⩽ x ⩽ 360° (ii) cot2y + 3cosec y = 3 π 1 (iii) cos(z + ) = − 0 ⩽ z ⩽ 2p 4 2 (i) Prove that sec2 x + cosec2 x = sec2 x · cosec2 x
(3 marks) (3 marks) (4 marks) (4 marks)
(ii) Hence or otherwise solve sec2 x + cosec2 x = 4tan2 x 90° ⩽ x ⩽ 270° 6
(4 marks)
(i) State the period of sin2x
(1 mark)
(ii) State the amplitude of 1 + 2cos3x
(1 mark)
(iii) Sketch the graph of a y = sin2x 0° ⩽ x ⩽ 180° b y = 1 + cos3x
0° ⩽ x ⩽ 180°
(4 marks)
(iv) State the number of solutions of sin2x − 2cos3x = 1
0° ⩽ x ⩽ 180°
(1 mark)
Chapter 2: Quadratic Functions
9