Cambridge Additional Mathematics

Answers 479

REVIEW SET 8B

1a 72 ± b 225 ± c 140 ± d 330 ±

2

3acos(^32 ¼)=0, sin(^32 ¼)=¡ 1

bcos(¡¼ 2 )=0, sin(¡¼ 2 )=¡ 1

4asin(¼¡p)=m bsin(p+2¼)=m

ccosp=

p

1 ¡m^2 dtanp=p m

1 ¡m^2

5a i 60 ± ii ¼ 3 b ¼ 3 units c ¼ 6 units^2

7 sinμ=

p 21

5 , tanμ=¡

p 21

2 , secμ=¡

5

2 ,

cosecμ=p^521 , cotμ=¡p^221

8a 212 b 112 c ¡^12

9aμ¼ 0 : 841 or 5 : 44 bμ¼ 3 : 39 or 6 : 03

cμ¼ 1 : 25 or 4 : 39

10 perimeter¼ 34 : 1 cm, area¼ 66 : 5 cm^2

11 r¼ 8 : 79 cm, area¼ 81 : 0 cm^212 a 0 b sinμ

13 sin®=

p 91

10 , cos®=¡

3

10 , tan®=¡

p 91

3 ,

cosec®=p^1091 , cot®=¡p^391

EXERCISE 9A

1aperiodic bperiodic c periodic

dnot periodic eperiodic f periodic

gnot periodic hnot periodic

2a

bA curve can be fitted to the data.

cThe data is periodic.

i y=32(approx.) ii ¼ 64 cm

iii ¼ 200 cm iv ¼ 32 cm

3a

Data exhibits periodic behaviour.

b

Not enough information to say data is periodic.

EXERCISE 9B

1a

b

c

d

e

f

2aa=2 b a=5 ca=11

3ab=3 b b=5 cb=6 d b=4

4ac=3 b c=¡ 1 cc=5

5a

3

-3

¼¼ 22 ¼¼

y

x

y = 3_¡¡¡sinx

O 33 ¼¼ 44 ¼¼

4

-4

¼¼ 22 ¼¼

y

y = 4_¡¡¡sinx

O 33 ¼¼ 44 ¼¼ x

10

20

30

40

50

60

50 100 150 200 250 300 350 400

height above

ground

()cm

O

distance travelled cm()

-1

1

2 4 6 8 10 12

y

O x

2

4

6

8

10

2 4 681012

y

O x

1

-1

x

y

y=¡¡¡sin3x

O ¼¼ 22 ¼¼ 33 ¼¼ 44 ¼¼

1

-1

x

y y=¡¡¡sin4x

O ¼¼ 22 ¼¼ 33 ¼¼ 44 ¼¼

3

2

1

y

¼ 2 ¼ x

y=¡¡¡¡¡sinx+2

O 3 ¼ 4 ¼

-1

-2

-3

y

x

¼ 2 ¼

y=¡¡¡¡¡sinx-3

3 ¼ 4 ¼

-4

O

2

-2

¼ 2 ¼

y

x

y=3_¡¡¡sinx-1

-4

O

y

x

O

cyan magenta yellow black

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100 100
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100 100 IB HL OPT
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