qb chapter 09

© Arah Pendidikan Sdn Bhd 1 Mathematics SPM

Chapter 9 Trigonometry II

Objective Questions

1 The following diagram shows a unit circle.

Find the value of cos θ.A 0.7623 C –0.7623B 0.6754 D –0.8860

2 The following diagram shows a unit circle.

Which of the following is true?A tan q° = 1.732 C cos q° = –0.8660B sin q° = 0.5 D cos q° = 0.5

3 The following diagram shows angles θ and α in the Cartesian plane.

Given that tan α = x, find the value of tan θ in terms of x.

A tan θ = x C tan θ = 1–x

B tan θ = –x D tan θ = –1–x

0

y

x

B(�0.5, �0.8660)

0

q°

0

0

θαx

y

0

θ1

y

x

A(�0.7623, 0.6754)


4 Given that cos p° = m for 0 � p � 90, find the value of cos(180° � p°).

A – C –m

B D m

5 Given that cos θ is negative, in which quadrant is θ situated?A I and III C II and IVB II and III D III and IV

6 Given that tan θ is positive, in which quadrant is θ situated?A I and III C II and IVB II and III D III and IV

7 Given that sin x° = –0.9272 and x lies in quadrant IV, the value of x isA 68 C 248B 112 D 292

8 Given that tan y° = –0.6249, the values of y between 0° and 360° areA 148 and 328 C 32 and 328B 148 and 212 D 32 and 212

9 If cos x° = cos 42° and 90° � x° � 360°, the value of x isA 138 C 222B 142 D 318

10 Without using tables or calculators, find the value of 7 cos 240° � 2 tan 225°.A –5.5 C 1.5B –3.5 D 5.5

11 Without using tables or calculators, find the value of 5 cos 180° � 4 sin 270°.A 9 C 1B 5 D –1

12 In the diagram below, BCD is a straight line.

Find the value of cos x°.A –0.8 C 0.5B –0.6 D 1

x°

B C D

A

4 cm5 cm

1––m

1––m


10 cm

CBA

D

x °

y°

13 In the diagram below, LMN is a straight line and MN = ON.

The value of tan x° isA –1 C 0.71B –0.71 D 1

14 In the diagram below, LMNY is a straight line and LM = MN.

Find the value of tan p°.

A –3–4

C 3–4

B –3–5

D 4–3

15 In the diagram below, ABC is a straight line.

Given that sin x° = 4–5

and tan y° = 1, calculate the length of ABC.A 14 cm C 16 cmB 15 cm D 17 cm

16 Which of the following graphs represents y = –sin θ?

A C

B D

L

Z

Y

X

NM

5 cm

10 cm

3 cm

p°

360°

270°

180°90°

0θ

�1

1

y

360°

270°

180°90°0

θ

�1

1

y

360°

270°

180°

90°

0θ

�1

1

y

360°

270°

180°

90°0θ

�1

1

y

L M N

O

x°6 cm


17 The following diagram shows the graph of a trigonometric function.

What trigonometric function is represented by the graph?A y = tan θ C y = –tan 2θB y = –tan θ D y = –tan 3θ

18 The diagram below shows the graph of y = cos 2θ.

The value of x isA 45° C 90°B 60° D 100°

19 The diagram shows the graph of y = 2 sin θ.

The value of p is

A 1–2

C 11–2

B 1 D 2

20 The diagram below shows the graph of a trigonometric function.

State the equation of this function.A y = tan θ C y = sin 2θB y = sin θ D y = –cos 2θ

90°0 θ

y

135°0 θ

�1

1

y

x

360°180°0θ

�p

p

y

180°45°0θ

�1

1

y


Subjective Questions

1 Draw and label each of the following positive angles in a unit circle.(a) 98°(b) 225.6°(c) 300° 25′

2 Without using tables or calculators, find the values of sine, cosine and tangent for each ofthe following cases.(a) 240°(b) 315°

3 Determine whether the value of each of the following is positive or negative.(a) cos 317°(b) tan 97°(c) sin 260°

4 Without using tables or calculators, find the values of the following.(a) 8 sin 270° � 3 tan 135°(b) 6 sin 150° � 4 tan 225°(c) 6 cos 30° � 2 tan 240°

5 Given that cos x° = –0.8910 and 180° � x° � 360°, find the value of x.

6 Given that tan p° = 0.7265 and 0° � p° � 360°, find the values of p.

7 In the diagram below, ∠ MON = 90° and MX = XO = OZ = ZN = 3 cm.

Calculate(a) the length of XN,(b) cos ∠ MZN.

Y

3 cm

3 cm

3 cm3 cmM X O

Z

N


8 In the diagram below, ∠ PSQ = 45°, PS = 5 cm and PR = 12 cm.

Calculate(a) the length of RS,(b) sin ∠ PRS,(c) ∠ QSR.

9 Sketch the graphs of the following trigonometric functions.(a) y = 3 sin x(b) y = 2 cos x � 1

10 The diagram below represents the graph of y = cos 3θ.

Find the value of φ.

P Q R12 cm

5 cm

S

45°

φ

60°

30°0 θ

�1

1

y

qb chapter 09

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