ECAT Mathematics
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ECAT Mathematics
Chapter 9: Fundamentals of Trigonometry
92 Questions
90 Minutes
Pass: 60%+
ECAT Prep
0
sin^2θ + cos^2θ =
A
0
B
1
C
2
D
sinθcosθ
1
One radian is the angle subtended at center by arc equal to:
A
Diameter
B
Radius
C
Circumference
D
Half circumference
2
π radians = ?
A
90°
B
180°
C
360°
D
270°
3
2π radians = ?
A
90°
B
180°
C
360°
D
270°
4
sin 0° =
A
0
B
1
C
−1
D
undefined
5
cos 0° =
A
0
B
1
C
−1
D
undefined
6
tan 90° =
A
0
B
1
C
∞ (undefined)
D
−1
7
sin 30° =
A
√3/2
B
1/2
C
√2/2
D
1
8
cos 60° =
A
√3/2
B
1/2
C
1
D
0
9
tan 45° =
A
0
B
1/2
C
1
D
√3
10
sin 90° =
A
0
B
1/2
C
√2/2
D
1
11
cos 90° =
A
0
B
1
C
−1
D
1/2
12
cosecant csc θ = 1/?
A
sinθ
B
cosθ
C
tanθ
D
cotθ
13
secant sec θ = 1/?
A
sinθ
B
cosθ
C
tanθ
D
cotθ
14
cotangent cot θ = 1/?
A
sinθ
B
cosθ
C
tanθ
D
secθ
15
tan θ = ?
A
cosθ/sinθ
B
sinθ/cosθ
C
sinθ×cosθ
D
1/sinθ
16
1 + tan^2θ =
A
sec^2θ
B
csc^2θ
C
cos^2θ
D
sin^2θ
17
1 + cot^2θ =
A
sec^2θ
B
csc^2θ
C
tan^2θ
D
sin^2θ
18
In which quadrant are both sin and cos positive?
A
II
B
I
C
III
D
IV
19
In Quadrant II, which trig function is positive?
A
sin
B
cos
C
tan
D
sec
20
In Quadrant III, which functions are positive?
A
sin and cos
B
tan and cot
C
sin only
D
cos only
21
In Quadrant IV, which is positive?
A
sin
B
cos
C
tan
D
cot
22
ASTC mnemonic stands for (quadrant-wise positivity):
A
All, Sin, Tan, Cos
B
All, Some, The, Cos
C
All, Sin, Tan, Cosec
D
All Students Take Calculus
23
sin(−θ) =
A
sinθ
B
−sinθ
C
cosθ
D
−cosθ
24
cos(−θ) =
A
cosθ
B
−cosθ
C
sinθ
D
−sinθ
25
Arc length s = rθ where θ is in:
A
Degrees
B
Radians
C
Gradians
D
Minutes
26
Area of sector = (1/2)r²θ where θ is in:
A
Degrees
B
Radians
C
Arcminutes
D
Any unit
27
Convert 60° to radians:
A
π/6
B
π/3
C
π/4
D
π/2
28
Convert π/6 to degrees:
A
30°
B
45°
C
60°
D
90°
29
sin 45° =
A
1/2
B
√3/2
C
√2/2
D
1
30
cos 30° =
A
1/2
B
√3/2
C
√2/2
D
1
31
sin 60° =
A
1/2
B
√3/2
C
√2/2
D
1
32
tan 30° =
A
1
B
√3
C
1/√3
D
√3/2
33
tan 60° =
A
1
B
√3
C
1/√3
D
√3/2
34
sin 0° + cos 0° =
A
0
B
1
C
2
D
√2
35
The period of sin(x) is:
A
π
B
2π
C
π/2
D
4π
36
The period of tan(x) is:
A
π
B
2π
C
π/2
D
4π
37
In a right triangle with hypotenuse 5 and opposite 3, sin θ =
A
3/5
B
4/5
C
3/4
D
5/3
38
In same triangle, cos θ =
A
3/5
B
4/5
C
3/4
D
5/4
39
tan θ in that triangle:
A
3/4
B
4/3
C
3/5
D
4/5
40
Reference angle for 150° is:
A
30°
B
60°
C
150°
D
120°
41
sin 150° =
A
−1/2
B
1/2
C
−√3/2
D
√3/2
42
cos 120° =
A
1/2
B
−1/2
C
√3/2
D
−√3/2
43
Domain of sin(x):
A
[−1,1]
B
(−π/2,π/2)
C
All real numbers
D
[0,2π]
44
Range of sin(x):
A
(−∞,∞)
B
(−1,1)
C
[−1,1]
D
[0,1]
45
The function sin θ = O/H, where O = opposite and H =
A
Adjacent
B
Hypotenuse
C
Height
D
Horizontal
46
The function cos θ = A/H, where A = adjacent, H = ?
A
Opposite
B
Adjacent
C
Hypotenuse
D
Horizontal
47
θ = 270° in radians:
A
3π/2
B
π
C
2π
D
3π
48
The angle subtended by complete circle:
A
π rad
B
2π rad
C
π/2 rad
D
3π/2 rad
49
sin(90°−θ) =
A
sinθ
B
−cosθ
C
cosθ
D
−sinθ
50
cos(90°−θ) =
A
cosθ
B
sinθ
C
−sinθ
D
−cosθ
51
Sexagesimal system measures angles in:
A
Radians
B
Degrees, minutes, seconds
C
Gradians
D
Turns
52
1 degree = ? minutes:
A
100
B
60
C
30
D
360
53
1 minute = ? seconds:
A
60
B
100
C
30
D
10
54
The radian measure of 1 revolution (360°):
A
π
B
3π/2
C
2π
D
4π
55
sin²θ = ?
A
1+cos2θ)/2
B
(1−cos2θ)/2
C
cos2θ
D
sin2θ
56
cos²θ = ?
A
(1−cos2θ)/2
B
(1+cos2θ)/2
C
sin2θ
D
tan2θ
57
In right triangle: hyp²=adj²+opp². This is:
A
Law of sines
B
Pythagorean theorem
C
Law of cosines
D
Trigonometric identity
58
The angle whose sin = 1 is:
A
0°
B
90°
C
180°
D
270°
59
The angle whose cos = −1 is:
A
0°
B
90°
C
180°
D
270°
60
Trigonometric functions are defined for angles in:
A
First quadrant only
B
All quadrants
C
Only acute angles
D
Only obtuse angles
61
sec θ is undefined when cos θ =
A
1
B
−1
C
0
D
1/2
62
csc θ is undefined when sin θ =
A
1
B
−1
C
0
D
1/2
63
cot θ = cos θ/?
A
tan θ
B
cos θ
C
sin θ
D
sec θ
64
sin θ/cos θ =
A
cot θ
B
sec θ
C
tan θ
D
csc θ
65
For angle 30°-60°-90° triangle, sides are in ratio:
A
1:1:√2
B
1:√3:2
C
1:2:3
D
2:√3:1
66
For 45°-45°-90° triangle, sides in ratio:
A
1:1:√2
B
1:√3:2
C
2:1:√3
D
√2:1:1
67
sin(180°+θ) =
A
sinθ
B
−sinθ
C
cosθ
D
−cosθ
68
cos(180°+θ) =
A
cosθ
B
−cosθ
C
sinθ
D
−sinθ
69
sin(360°−θ) =
A
sinθ
B
−sinθ
C
cosθ
D
−cosθ
70
cos(360°−θ) =
A
cosθ
B
−cosθ
C
sinθ
D
−sinθ
71
The sign of tan in QII is:
A
Positive
B
Negative
C
Zero
D
Undefined
72
Period of cos(x):
A
π
B
2π
C
π/2
D
4π
73
sin 180° =
A
0
B
1
C
−1
D
1/2
74
cos 180° =
A
0
B
1
C
−1
D
1/2
75
tan 0° =
A
0
B
1
C
−1
D
undefined
76
√3 × sin 30° =
A
√3/2
B
1
C
√3
D
3/2
77
sin 30° + cos 60° =
A
1
B
0
C
√3
D
1/2
78
tan 45° + cot 45° =
A
1
B
2
C
0
D
√2
79
Degree measure corresponding to 5π/6:
A
120°
B
150°
C
90°
D
135°
80
The angle of 225° lies in quadrant:
A
I
B
II
C
III
D
IV
81
sin(π/4) + cos(π/4) =
A
0
B
1
C
√2
D
√2/2
82
The unit circle has radius:
A
π
B
2π
C
1
D
1/2
83
On unit circle, coordinates of point at angle θ are:
A
(sinθ,cosθ)
B
(cosθ,sinθ)
C
(tanθ,cotθ)
D
(1,θ)
84
sin²30°+cos²30° =
A
3/4
B
1
C
1/4
D
√3/2
85
The number of degrees in one radian is approximately:
A
57.3°
B
45°
C
90°
D
180°/π≈57.3°
86
sec 0° =
A
0
B
1
C
−1
D
undefined
87
csc 90° =
A
0
B
1
C
−1
D
undefined
88
An angle is in standard position when its vertex is at:
A
Any point
B
Origin with initial side on positive x-axis
C
Center of a circle
D
The end of number line
89
Coterminal angles differ by:
A
90°
B
180°
C
360° (or 2π)
D
Any amount
90
sin(−30°) =
A
1/2
B
−1/2
C
√3/2
D
−√3/2
91
cos(−60°) =
A
−1/2
B
1/2
C
−√3/2
D
√3/2
0
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