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CHAPTER 9: TRIGONOMETRY II
EXERCISE 1
1. In Diagram 1, ABC is a straight line. D 6 cm 10 cm xo A B C DIAGRAM 1 Find the value of sin xº. 2. In Diagram 2, ABC is a straight line. D 5 cm 13 cm yo A B C DIAGRAM 2 Find the value of cos yº. 3. Find the value of tan 0o + 2 sin 90o – 3 (cos 180o). 4. Diagram 3 shows the curve y = f(x)?
1 y=f(x)
0 90 180 270 360 -1 DIAGRAM 3
State the name of the curve y = f(x).
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5. State the angle in the first quadrant that is equivalent to 200º. 6. In Diagram 4, BCD is a straight line.
A 7 cm 5 cm 3 cm θ
B C D DIAGRAM 4 Find tan θ. 7. In Diagram 5, BCD is a straight line.
A 2 cm θ
B 2 cm C 2 cm D DIAGRAM 5
Find cos θ.
8. In Diagram 6, ABC is a right angled-tringle. DIAGRAM 6
Given that sin θ = 54 , find the length of BC
θ
A
25cm
C
B
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9. In Diagram 7, BDC is a straight line.
DIAGRAM 7
Given that sin x = 53 and tan y =
54 , find, the length, in cm, of BC.
10. In diagram 8, BCD is a straight line.
DIAGRAM 8 Given that cos y = 0.6, find the value of cos x.
10 cm x y
B D C
A
16 cm x y 20 cm
B C D
A
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CHAPTER 9: TRIGONOMETRY II
EXERCISE 2
1. In Diagram 1, PQR is a straight line and 1
3PQ QR=
Find the value of sin xo. Answer: ………………………………..
2. In Diagram 2, PQR is a straight line. Find the length of QS, in cm.
Answer : ………………………………….
3. Given that tan θ = 0.7382 and 180o ≤ θ ≤ 360o, find the value of θ. Answer : ……………………….………
8 cm
6 cm
DIAGRAM 2
Q
P S
R
8 cm xo
P 5 cm Q R
S
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4. In Diagram 3, O is the centre of a unit circle. Find the value of tan xo.
Answer: ……………………………..
5. In Diagram 4, PQRS is a rectangle. Find the value of cos xo.
Answer : ………………………………
x°
12 cm
10 cm
DIAGRAM 4
Q
S R
P
M
-0.8,0.6( )
DIAGRAM 3
-1
-1 1 xO
y
1
xo
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DIAGRAM 5
O x
y
1
-1-0.5
p
12 cm
x°
DIAGRAM 7QP R
S
6. Diagram 5 shows the graph of y = cos xo. Determine the value of p .
Answer : …………………………….
7. In Diagram 6, PTU and PQRS are straight lines. Find the value of cos xo.
Answer : ……………………………
8. In Diagram 7, PQR is a straight line.
It is given that 4cos .5
ox =− Find the length of SP, in cm.
Answer : ………………………….
x°
15 cm
17 cm
DIAGRAM 6
T
RP
S
U
Q
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9. In Diagram 8, PRS is a straight line and RS = 12 cm. Find the value of sin xo.
Answer : ……………………………..
10. In Diagram 9, QRST is a straight line. Find the value of sin xo. Answer : ……………………………..
8 cm
21 cm
17 cm
x°
DIAGRAM 9
R SQ T
P
25 cm
15 cm
15 cm
x°
DIAGRAM 8
PS
T
R
Q
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CHAPTER 9: TRIGONOMETRY II
DIAGNOSTIC TEST
1. Given that, sin θ = 53 and oo 18090 ≤≤ θ , find the value of cos θ .
A 54
B 35
C 54
−
D 43
−
2. Determine the equivalent of sin 46o 24’ .
A cos 133o 36’ B sin 133o 36’ C sin 226o 24’ D sin 313o 36’
3. Given that, cos 45o = 0.7071. Find the value of cos 225o
A -0.7071 B -0.6929 C 0.6929 D 0.7071 4. In Diagram 1, BCD is a straight line. Find the value of cos ro.
DIAGRAM 1
A 54
−
B 53
C 53
−
D 43
−
ro B 4 cm A C 3 cm D
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5. By using a calculator, find the value of cos 216o 24’ A 0.8048 B 0.8049 C -0.8049 D -0.8048 6.
In Diagram 6, PQR is a straight line and PR = 10 cm. Find the value of cos xo.
A 513
−
B 1213
−
C 513
D 1213
DIAGRAM 6
12 cm
x°
S R
P
Q
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7. In Diagram 7, PRS is a straight line and 3tan
4x= .
Find the value of tan yo.
A 12
−
B 58
−
C 12
D 58
8.
Which of the following graphs represents y = cos x ?
x
x
y y
yy
O
O
O
O
1
90 180
1
-1
-190
1
90
-1
1
-1
90 180
180180
A B
C D
y°
6 cm
5 cm
DIAGRAM 7
x°
R
P Q
S
T
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9. In Diagram 9, O is the centre of a unit circle. Determine the value of sin xo. A 0.5 B -0.866 C -1.732 D -0.5774
10. Given that cos x = cos 110o and 180o ≤ x ≤ 360o, find the value of x. A 200o B 250o C 290o D 340o
DIAGRAM 9
x
y
x°
0.5,-0.866( )
O
