18[a math cd]

1 Penerbitan Pelangi Sdn. Bhd.

Paper 1

1. sin r = y-coordinate = 0.6428Answer: B

2. sin p = y-coordinate = 0.866cos p = x-coordinate = 0.5

tan p = y-coordinatex-coordinate = 0.866 0.5 = 1.732Answer: A

3. sin t = y-coordinate = 0.9659cos t = x-coordinate = 0.2588

tan t = y-coordinatex-coordinate = 0.9659 0.2588 = 3.732Answer: D

4. sin = y-coordinate = 0.9903cos = x-coordinate = 0.1392

tan = y-coordinatex-coordinate = 0.9903 0.1392 = 7.114Answer: C

5.

x

y

yx

O

sin y = sin (180 y) = sin x = pAnswer: A

6.

x

y

y

x O

cos y = cos (y 180) = cos x = tAnswer: C

7.

x

y

x

180 + x

O

sin (180 + x) = sin x = qAnswer: B

8.

x

y

x360 x

O

tan (360 x) = tan x = pAnswer: B

CHAPTER

18 Trigonometry IICHAPTER

2 Mathematics SPM Chapter 18

Penerbitan Pelangi Sdn. Bhd.

9.

x

y

O x

y

O

Answer: D

10.

x

y

O

x

y

O

Answer: B

11.

x

y

O

x

y

O

cos < 0sin < 0

Answer: C

12.

x

y

O

x

y

O

tan < 0cos > 0

Answer: A

13. sin 0 = 0

180 36090 270

1

1

y

x0

sin 90 = 1sin 180 = 0sin 270 = 1sin 360 = 0

Answer: A

14. cos 0 = 1

180 36090 270

1

1

y

x0

cos 90 = 0cos 180 = 1cos 270 = 0cos 360 = 1

Answer: D

15. tan 0 = 0

180 36090 270

y

x0

tan 90 = tan 180 = 0tan 270 = tan 360 = 0Answer: B

Paper 1

1.

S

R

Q

P

TU

3 cm

5 cm 4 cm

13 cm5 cm

12 cm

sin SRT = STRS 45 =

4RS

RS = 5 cm RT = 52 42 = 3 cm RU = 4 3 = 12 cm QR = 132 122 = 5 cm tan q = tan RQU = RUQR = 125Answer: D



2. y = cos x cos 0 = 1 cos 180 = 1 cos 360 = 1

y

x1

10 180 360

Answer: D

3. y

xPy

Q(4, 3)

4

3

O

OQ2 = PQ2 + PO2 OQ = 32 + 42 = 5 units sin y = sin POQ = PQOQ = 35Answer: C

4. sin 225 = cos 225 = 0.7071Answer: C

5. cos x = 817 EFFH =

817

\ EF = 8, FH = 17 EH = 172 82 = 15tan y = EHEF = 158Answer: A

6. y = sin xWhen x = 360, y = sin 360 = 0Answer: D

7.

x

yP Q R

S

25 cm

sin x = PQPS PQ25 =

45 PQ = 45 25 = 20 cm QS 2 = SP2 PQ2

QS = 252 202 = 15 cm

tan y = QSQR 15QR =

158 QR = 8 cmHence, PQR = 20 + 8 = 28 cmAnswer: B

8.

x

y

12

513O

x

tan x = tan (360 x) = 512Answer: B



9. y = tan 2x tan 0 = 0 tan 2(45) = tan 90 =

y

x0 45

Answer: C

10. cos p = x-coordinate = 0.26sin q = y-coordinate = 0.50cos p + sin q = 0.26 + 0.50 = 0.76Answer: B

11.

x

y

O

6255

cos = 0.4552 = 180 + 6255 = 24255Answer: B

12.

12 cm

5 cm

E

F

G

H

EG 2 = EF 2 + FG2 EG = 122 + 52 = 13 cm cos = cos EGF = FGEG = 513Answer: C

13. y = sin 2x sin 0 = 0 sin 2(45) = sin 90 = 1 sin 2(90) = sin 180 = 0sin 2(270) = sin 540 = 0

90 360180 2700

1

1

x

y

Answer: A

14. S

R

T

QP

1715

8

PQ = 172 152 = 8 cos RST = cos TQR = cos PQT = 817Answer: D

15. y = tan x tan 0 = 0 tan 90 = tan 180 = 0

180900x

y

Answer: B



16. P

Q R S

15 m

12 m

cos PRS = cos PRQ 45 =

12PR

PR = 15 m PQ2 = 152 122 PQ = 225 144 = 9 mAnswer: D

17.

x13 cm10 cm

Q P

R

S

RP = 5 cm PQ2 = QR2 RP 2 PQ = 132 52 = 12 cm

sin x = PQQR

= 1213Answer: C

18.

PQ15 cm 15 cm

17 cm

R

S

y

RS2 = QS2 QR2 RS = 172 152 = 8 cm tan y = tan SQR = RSQR = 815Answer: C

19. y = cos x cos 0 = 1 cos 90 = 0 cos 180 = 1

90 1800

1

1

x

y

Answer: B

Paper 1

1.

x

y

O70

x

y

O70

cos x = 0.3420 x = 70, (360 70) x = 70, 290Answer: C

2.

x

y

O56x

y

O 56

sin x = 0.8290 x = (180 + 56), (360 56) x = 236, 304Answer: A

3.

x

y

O57

x

y

O 57

tan q = 1.540 q = (180 57), (360 57) q = 123, 303Answer: A



4.

x x

y y

O O25

25

tan y = 0.4663 y = (180 25), (360 25) y = 155, 335Answer: D

5.

x x

y y

O O27 27

sin y = sin 27 y = (180 + 27), (360 27) y = 207, 333Answer: D

6.

x x

y y

O O 4545

sin p = cos p p = (180 45), (360 45) p = 135, 315Answer: C

7.

x x

y y

O O60

60

cos t = sin 150 = sin 30 = 0.5 t = 60, (360 60) t = 60, 300Answer: B

8.

y

60

P S

Q

R

cos y = cos 60 = 0.5Answer: C

9.

y

SRP

T

12 cm

5 cm

TR2 = TP2 + PR2

TR = 122 + 52 = 13 cm sin y = sin PRT = TPTR = 1213Answer: D

10.

m110

35F G H

J

JGH = 180 1102 = 35tan m = tan 35 = 0.700Answer: A



11.

x30

L

M N P

4 cm6 cm

sin LNM = LMLN sin 30 = LM4 LM = 4 sin 30 = 4 0.5 = 2 cm sin x = LMLP = 26 = 13Answer: B

12.

r

10 cm

6 cm

M N P

Q

cos r = 12 cos QNM = 12 MNQN =

12 MN = 12 6 = 3 cm QM 2 = QN 2 MN2 = 62 32 = 27 PQ2 = QM 2 + PM2 = 27 + 132 = 196 PQ = 196 = 14 cmAnswer: B

13.

y

E F

H

G

4 cm

6 cm

tan EHF = EFFH 4FH =

49 FH = 9 cm FG = 9 6 = 3 cm EG2 = FG2 + EF2 EG = 32 + 42 = 5 cm cos y = cos EGF = FGEG = 35Answer: B

14. L

H J K

5 cm

5 cm3 cm

Using Pythagoras triple,LH = 4 cmsin LJK = sin LJH = LHLJ = 45Answer: B



15.

P Q R S

T

13 cm

135455 cm

TQ = 5 cm PQ2 = PT 2 QT 2 PQ = 132 52 = 12 cmHence, PQR = 12 + 5 = 17 cmAnswer: C

16.

120 608 cmP Q R

T

cos TQR = QTQR cos 60 = QT8 QT = 8 cos 60 = 8 0.5 = 4 cmAnswer: B

17.

15 cm

9 cm

QP R

S

PS2 = PQ2 QS2 PS = 152 92 = 12 cm tan RQS = tan PQS = PSQS = 129 = 43Answer: D

18.

8 cm

10 cm

T R

Q

P

cos PTR = TRPT 8PT =

817 PT = 17 cm PR2 = PT 2 TR2 PR = 172 82 = 15 cmHence, QR = 15 10 = 5 cmAnswer: B

19.

xy

4 cm

15 cm

R

Q

PT

U

tan x = PQQT 4QT =

12 QT = 2 4 = 8 cm RT 2 = RQ2 + QT2 RT = 152 + 82 = 17 cm cos y = cos QTR = QTRT = 817Answer: A



20.

P Q

R

S

9 cm

cos QPS = PQPS 9PS =

35 PS = 5 93 = 15 cm QS2 = PS2 PQ2 QS = 152 92 = 12 cmHence, QR = 122 = 6 cmAnswer: D

21. m

F

G

E8 cm

H

tan FEG = FGFE FG8 =

158 FG = 15 cm EG2 = FG 2 + FE 2 EG = 152 + 82 = 17 cm cos m = cos EGF = FGEG = 1517Answer: D

22.

m

nP T

26 cm

R

Q

S

sin m = QRPQ QR26 =

513 QR = 513 26 = 10 cm PR2 = PQ2 QR2 PR = 262 102 = 24 cm TR = 242 = 12 cm

tan n = TRRS 12RS = 2

RS = 122 = 6 cmHence, QRS = 10 + 6 = 16 cmAnswer: C

23. y = cos x cos 0 = 1 cos 90 = 0 cos 180 = 1 cos 270 = 0 cos 360 = 1

180 360

1

1

y

x0

Answer: B

10

Mathematics SPM Chapter 18


24. y = sin x2 sin 1 02 2 = 0 sin 1 902 2 = 0.707 sin 11802 2 = 1

y

x1

10 90 180

Answer: C

25. y = sin 3x sin (0) = 0 sin 3(30) = sin 90 = 1 sin 3(60) = sin 180 = 0 sin 3(90) = sin 270 = 1 sin 3(120) = sin 360 = 0

60 120

1

1

y

x0

Answer: D

26. y = tan 2x tan 0 = 0 tan 2(45) = tan 90 = tan 2(90) = tan 180 = 0

y

x0 45 90

Answer: A

27. sin 45 = cos 45 = 0.7071sin 225 = cos 225 = 0.7071Answer: B

28. sin 0 = 0 sin 3(90) = sin 270 = 1 sin 3(180) = sin 540 = 0Hence, y = sin 3xAnswer: D

29. y = cos 2y = cos 2(135) = cos 270 = 0Answer: A

18[a math cd]

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