Page 51 - ACE YR IGCSE A TOP APPR' TO ADD MATH

5. 3(1 − cos x) − 5 cos x = 5 (b)
2
3 − 3 cos x − 5 cos x − 5 = 0 y
2
3 cos x + 5 cos x + 2 = 0 2
2
(3 cos x +2 )(cos x + 1) = 0
2
cos x = − or cos x = −1
3 –2π –π 0 π 2π x
x = −131.81° or x = −180°
[4] –2
6. (a) 5 sin q − 2 = 0
sin q = 2 –4
5
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q = 0.412 rad or q = 2.73 rad –6
[4]
1
(b) tan 2q – π 2 = 0.5 –8
4
π [3]
2q – = 0.4636, 3.6052, 6.747, 9.888
4 9. (a) cot x − tan x
2
2
2
2
q = 0.625 rad, 2.20 rad, 3.77rad, = cosec x − 1 − (sec x − 1)
2
2
5.34 rad = cosec x − sec x
[4] 1 – 2 sin x [3]
2
7. cos x = 1 (b) sin x + cos x
2 sin x + cos x – 2 sin x
2
2
2
x = 60° = sin x + cos x
2
2
cosec x + sec x = cos x – sin x
= 1 + 1 sin x + cos x
cos x sin x (cos x + sin x)(cos x – sin x)
2 = sin x + cos x
= 2 +
√3 = cos x – sin x
= 6 + 2√3 or 3.15 [4]
2
2
3 [4] (c) tan x sin x
= (sec x − 1)(1 − cos x)
2
2
= sec x − sec x cos x − 1 + cos x
2
2
2
2
8. (a)
2
= 1 + tan x – 1 1 × cos x – sin x
2
2
2
2
y cos x
= 1 + tan x – 1 – sin x
2
2
= tan x – sin x
2
2
[4]
3
u
u
10. y = 3 sin x
2
[3]
2
11. (a)
y
2
x
π 2π
[3]
x
π 2π
[2]
Answers 191

Answers Add Math.indd 191 14/03/2022 12:29 PM