Chapter No. 09
FUNDAMENTALS OF TRIGONOMETRY
1.
Direction
__________
of
Qibla
is
found
by
using
a) Plane Geometry
b) Spherical Trigonometry
c) Plane Trigonometry
d) Analytical Geometry
e) None of these
Answer:
b
2.
a
1rt. angle = __________
a)
b)
c)
d)
e)
90o
180o
270o
190o
None of these
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Measure of the central angle of an are of a
circle whose length is equal to the radius of
the circle is known as _________
a) 1 degree
b) 1 radian
c) 1 rt. angle
d) All of these
e) None of these
Answer:
b
8.
The circumference of a circle r is considered
as __________
a) 2 π r
b) π r
c) 3 π r
d) 4 π r
e) None of these
Answer:
a
9.
1 radian = __________
a) 57°17 ′45′′
b) 47o
c) 37o
d) 38o
e) None of these
Answer:
a
One degree is denoted by __________
a) 1 rad
b) 1’
c) 1”
d) 1o
e) None of these
Answer:
d
5.
7.
The union of two non-collinear rays which have
a common endpoint is called the ________
a) Angle
b) Radian
c) Degree
d) Minute
e) Second
Answer:
4.
a) centimeter
b) radian
c) degree
d) minute
e) none of these
Answer:
d
If a circle is divided into 360 parts, then the
angle subtended by each part at the center of the
circle is called __________
a) 1 radian
b) 1 degree
c) 1 angstrom
d) 1 minute
e) None of these
Answer:
b
3.
Answer:
a
th
6.
The 60 part of one degree is called one
____________
10.
1o = _________
a) 60′
b) 60′′
c) 3600′
d) 360′
e) None of these
Answer:
a
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106.
d) 1o
e) None of these
Answer:
c
1 + cot22 θ = _________ ?
a) sec θ
b) cosec2 θ
c) cosec22 θ
d) sec2 θ
e) none of these
Answer:
c
2
16.
13.
17.
d)
15.
, Cosθ is ___________
1
2
3
2
2
e)
2
Answer:
d) −
π
6
π
3
18.
b
c
a) 2π − a
b) 2π − (a + b)
c) 2π − (a + b + c)
d) a + b + c
e) 2d – 2b
Answer:
c
cm
π
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In the given figure the angle θ is __________
θ
cm
a) 1 rad
b) 1′
c) 1′′
c
a
cm
18
Answer:
d
One second is denoted by _______
e)
6
1
2
3
c)
2
π
An arc PQ is subtends and angle 600 at the
center of a circle of radius 1 cm. The length PQ
is ________
a) 60 cm
b) 30 cm
c)
π
b) −
2
3π
d)
4
e) None of these
Answer:
a
14.
= __________
If θ =
a)
180o = ________
a) π radian
b) 2 π radian
c)
4
a) 30o
b) 60o
c) 90o
d) 220o
e) None of these
Answer:
e
12.
The 60th part of one minute is called one
________
a) centimeter
b) radian
c) degree
d) minute
e) second
Answer:
e
π
19.
1′ = ________
a) 60o
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b) 60′′
c) 3600′′
d) 3600o
e) None of these
Answer:
b
B
θ
A
20.
a
c
C
b
a
c
c
b)
a
c
c)
b
b
d)
c
e) None of these
Answer:
a
What is the length of an arc of a circle of radius
5cm, whose central angle is of 140o ________
a)
a) 2.443 radians
b) 1.443 radians
c) 0.443 radians
d) 2 radians
e) None of these
Answer:
a
21.
In the given figure the angle a + b + c is
__________
24.
Four right angles are the angle of measure
________
B
a
a) 90o
b) 180o
c) 270o
d) 360o
e) 360′
Answer:
θ
b
θ
B
c
C
a) < BDC = θ
b) π − θ
c) 2π − θ
d) 2π + θ
e) < B
Answer:
c
22.
Two right angles are the angle of measure
_________
a) 180′′
b) 180′
c) 60o
d) 90o
e) 180o
Answer:
e
25.
d
In the figure the area of triangle ABC is
D
C
16
A
B
12
a) 28
b) 32
c) 96
d) 192
e) 182
Answer:
c
26.
For a right angled triangle ABC as shown in
the figure, we have Co secθ = _______
B
23.
For a right angled triangle ABC as shown in the
figure we have Sin θ = _______
a
c
θ
A
b
C
c
a)
a
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c
b
b
c)
c
+c
d)
−c
e) None of these
Answer:
a
Answer:
b)
27.
Sinθ
Cosθ
Cosθ
b)
Cosθ
1
c)
Sinθ
1
d)
Cosθ
e) None of these
Answer:
d
32.
In the figure, the shaded area is given by
A
Cotθ = ____________
Sinθ
Cosθ
Cosθ
b)
Sinθ
1
c)
Sinθ
1
d)
Cosθ
e) None of these
Answer:
b
Secθ = __________
a)
The system of measurement in which the angle
is measured in degrees, and its subunits,
minutes and seconds is called _________
a) Circular system
b) Sexagesimal system
c) MKS system
d) CGS system
e) None of these
Answer:
b
28.
31.
a
B
C
a) 25π / 4 − 6
b) 5π − 6
c) 25 / 4π
d) 6
e) 7π
Answer:
a
a)
33.
16 o 40 ′38′′ =
a) 140o
b) 17o
c) 16o
d) 60038′
e) 60038′′
Answer:
29.
a)
b)
c)
d)
e)
Answer:
e
34. Sin 2θ + Cos 2θ = _______, for all values of angle.
a) 1
a
b) 0
c) 1 + Tan 2θ
30.
The system of measurement in which the angle
d) – 1
is measured in radians is called _____
e) None of these
Answer:
a
a) Circular system
b)
c)
d)
e)
Sexagesimal system
MKS system
CGS system
None of these
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35.
In the figure the length of AB is
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c) 80o
d) – 80o
e) 190o
Answer:
C
45
A
6
36.
40.
Cot 180o = _________
a) 1
b) O
c) – 1
d) ∞
e) – 11
Answer:
d
41.
A radian is the measure of the central angle of
an arc of a circle whose length is equal to the
a) half of radius of the circle
b) diameter of the circle
c) radius of the circle
d) one third of radius of the circle
e) none of these
Answer:
c
42.
Sec 180o = _________
a
o
16 = ________
a) 960o
b) 960′
c) 57600′
d) 60038′
e) 60038′′
Answer:
37.
B
D
a) 7
b) 6 + 2
c) 6 + 2 2
d) 12
e) 13
Answer:
b
In the figure the angle A is (AB = AC = X)
a) 1
b) 0
c) – 1
d) ∞
e) None of these
Answer:
c
A
X
B
a) 50o
b) 60o
c) 90o
d) 120o
e) 180o
Answer:
38.
39.
X
C
X
43.
In the ∆ABC the angle α is
B
a
2a
b
o
A
e
The associated angle of 280o is
a) 100o
b) 10o
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30
a) 30o
b) 45o
c) 60o
d) 90o
e) 180o
Answer:
Two right angles are equal to
a) 180′
b) 180′′
c) 648000′
d) 10800 ′′
e) 10800′
Answer:
c
0
44.
C
c
The central angle of an arc of a circle whose
length is equal to the radius of the circle is
called the
a) degree
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b) radian
c) minute
d) second
e) none of these
Answer:
b
63.
a)
o
59.
 180 
Convert 
 to radians
 π 
a) 0.94 radians
b) 1 radians
c) 3.97 radians
d) 4.57 radians
e) 3.54 radians
Answer:
b
60.
64.
o
1 = ________
a)
b)
π
180
180
π
θ = _______
1
φ
1
b)
r
r
c)
l
φ
d)
r
r
e)
φ
Answer:
b
5π
radians =
4
a) 360o
b) 335o
c) 270o
d) 225o
e) 125o
Answer:
radians
radians
1
radians
180π
d) 180π radians
e) π radians
Answer:
a
d
c)
65.
o
61
62.
 1
 22  =
 2
π
a) radians
2
π
b) radians
4
π
c) radians
8
d) 180π radians
e) π radians
Answer:
c
Convert radian measure
a) 24.32o
b) 24.97o
c) 4.96o
d) 1.97o
e) 23.42o
Answer:
The radian measure of the angle at the center
of circle of radius 12cm which cuts off an arc
18cm long.
a) 9.47 radians
b) 1.19 radians
c) 1.5 radians
d) 2.5 radians
e) None of these
Answer:
c
66.
150o =
5π
radians
6
2π
b)
radians
3
a)
4
to degree
3π
π
radians
4
d) 180π radians
e) π radians
Answer:
a
c)
a
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67.
The length of the arc cut off on a circle of radius
2π
6cm by a central angle of
radians
3
a) 12.566cm
b) 10.033cm
c) 12.113cm
d) 9.156cm
e) 6.56cm
Answer:
a
68.
a) positive
b) negative
c) both
d) not defined
e) none of these
Answer:
a
72.
In one hour, the hours hand of a clock turns
through
a)
o
80 =
b)
5π
radians
a)
6
4π
radians
b)
9
c)
c)
77.
78.
a)
π
radians
4
d) 180π radians
e) 2 π radians
Answer:
e
c)
71.
In the second quadrant Sinθ is ________
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8
π
6
radians
radians
Cosθ =
1
?
In the 2nd quadrant Sec θ is ________?
a) positive
b) negative
c) both
d) not defined
e) – 1
Answer:
b
70.
In one hour, the minutes hand of a clock turns
through
5π
radians
6
4π
b)
radians
9
π
radians
a) sin θ
b) tan θ
c) cos θ
d) sec θ
e) none of these
Answer:
e
69.
The radius of the circle when l = 3cm, θ = 3.4
radians.
a) 0.214 cm
b) 9.419 cm
c) 3.146 cm
d) 4.978 cm
e) None of these
Answer:
e
12
d) π radians
e) 2 π radians
Answer:
c
π
radians
4
d) 180π radians
e) π radians
Answer:
b
π
79.
In the 2nd quadrant Cot θ is _______ ?
a) positive
b) negative
c) both
d) not defined
e) < 1
Answer:
b
80.
In 15 minutes the hours hand of a clock turns
through
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Answer:
a
o
a) 7.5
b) 15o
c) 30o
d) 60o
e) 120o
Answer:
98.
a
cos 2
θ
2
+ sin 2
1
4
1
b)
2
c) 2
d) 0
e) 1
Answer:
θ
2
= _________
a)
82.
In the 3rd quadrant Sin θ is _______ ?
a) positive
b) negative
c) both
d) not defined
e) > 0
Answer:
b
93.
sec2 θ - tan2 θ = _______
a) – 1
b) cosec θ
c) tan θ
d) 1
e) – 11
Answer:
94.
95.
101.
d
102.
The area of a sector of a circular region of
radius r and the central angle of the sector θ
radians is
1
a) rθ 2
2
1
b) r 2θ
2
1
c) rθ
103.
2
d) r 2θ
e) rθ 2
Answer:
b
The area of a sector with a central angle of 1
radian in a circular region whose radius is 2m.
a) 2m2
b) 1m2
104.
c) 0.5m2
d)
e)
π
6
π
3
m2
m2
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e
− 3π
= _______ ?
2
a) 1
b) 0
c) – 1
d) 11
e) None of these
Answer:
a
Sin
Cos
− 3π
= _______ ?
2
a) 1
b) 0
c) – 1
d) 10
e) None of these
Answer:
b
Cos9π = _______ ?
a) 1
b) 0
c) – 1
d) 10
e) None of these
Answer:
c
Cosec2 θ - Cot2 θ = _______ ?
a)
b)
c)
d)
1
0
–1
Tan2 θ
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e) Sec2 θ
Answer:
105.
a
Cos22 θ = _______ ?
a) 1 – sin2 θ
b) 1 + sin2 θ
c) 1 – sin22 θ
d) 1 - sin θ
e) 1 + sin θ
Answer:
c
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