ECAT Mathematics
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ECAT Mathematics
Chapter 11: Trigonometric Functions and Graphs
83 Questions
90 Minutes
Pass: 60%+
ECAT Prep
0
The graph of y=sinx has amplitude:
A
π
B
1
C
2
D
2π
1
The graph of y=2sinx has amplitude:
A
1
B
2
C
π
D
2π
2
The period of y=sin(2x) is:
A
2π
B
π
C
4π
D
π/2
3
The period of y=cos(x/2) is:
A
π
B
2π
C
4π
D
π/2
4
The period of y=tan(x) is:
A
2π
B
π/2
C
π
D
4π
5
The range of y=3cosx is:
A
[0,3]
B
[−3,3]
C
(−3,3)
D
[−1,1]
6
The graph of y=sinx crosses x-axis at:
A
x=π/2+nπ
B
x=nπ
C
x=2nπ
D
x=π/4+nπ
7
Maximum value of y=sinx:
A
0
B
π
C
−1
D
1
8
Minimum value of y=cosx:
A
0
B
−1
C
1
D
−π
9
The phase shift of y=sin(x−π/2) is:
A
π/2 to the left
B
π/2 to the right
C
π to the right
D
No shift
10
y=sin(x+π/2) is the same as:
A
y=sinx
B
y=cosx
C
y=−sinx
D
y=−cosx
11
y=cos(x−π/2) is the same as:
A
y=cosx
B
y=sinx
C
y=−sinx
D
y=−cosx
12
Vertical shift in y=sinx+3 is:
A
3 units down
B
3 units up
C
3 units right
D
3 units left
13
The graph of y=tanx has vertical asymptotes at:
A
x=nπ
B
x=π/2+nπ
C
x=π/4+nπ
D
x=2nπ
14
Domain of y=tanx excludes:
A
x=nπ
B
x=π/2+nπ
C
All reals
D
x=2nπ
15
The graph of y=cosx is symmetric about:
A
The x-axis
B
The y-axis
C
Origin
D
y=1
16
The graph of y=sinx is symmetric about:
A
The x-axis
B
The y-axis
C
The origin
D
y=1
17
y=|sinx| has period:
A
π
B
2π
C
π/2
D
4π
18
The amplitude of y=−3sin(2x) is:
A
−3
B
3
C
2
D
6
19
Period of y=−3sin(2x):
A
π
B
2π
C
3π
D
6π
20
Maximum value of y=4cos(x)−2:
A
4
B
2
C
−6
D
−2
21
Minimum value of y=4cos(x)−2:
A
−4
B
−6
C
−2
D
2
22
General form y=Asin(Bx+C)+D: C/B represents:
A
Amplitude
B
Period
C
Phase shift
D
Vertical shift
23
The graph of y=sin(πx) has period:
A
1
B
2
C
π
D
2π
24
The graph of y=cotx has period:
A
π
B
2π
C
π/2
D
4π
25
y=cscx is the reciprocal of:
A
tanx
B
cosx
C
sinx
D
cotx
26
y=secx is the reciprocal of:
A
sinx
B
cosx
C
tanx
D
cotx
27
y=secx has vertical asymptotes at:
A
x=nπ
B
x=π/2+nπ
C
x=π/4+nπ
D
x=2nπ
28
y=cscx has vertical asymptotes at:
A
x=nπ
B
x=π/2+nπ
C
x=π/4+nπ
D
x=2nπ
29
The graph of y=sin(x) and y=cos(x) are related by horizontal shift of:
A
π/2
B
π
C
2π
D
π/4
30
In y=Asin(Bx), the period is:
A
A
B
B
C
2π/B
D
2πA/B
31
Amplitude of y=sin(x)/3:
A
3
B
1
C
1/3
D
π/3
32
Sketch of y=2sin(x/2): period=
A
4π
B
2π
C
π
D
8π
33
The graph of y=−sinx is a reflection of y=sinx about:
A
y-axis
B
x-axis
C
line y=x
D
Origin
34
The graph of y=sin(−x) is the same as:
A
y=sinx
B
y=−sinx
C
y=cosx
D
y=−cosx
35
The graph of y=cos(−x) is the same as:
A
y=−cosx
B
y=sinx
C
y=cosx
D
y=−sinx
36
The maximum points of y=sinx occur at:
A
x=0+2nπ
B
x=π/2+2nπ
C
x=π+2nπ
D
x=3π/2+2nπ
37
The minimum points of y=sinx occur at:
A
x=π/2+2nπ
B
x=π+2nπ
C
x=3π/2+2nπ
D
x=2nπ
38
The maximum of y=cosx occurs at:
A
x=π/2+2nπ
B
x=2nπ
C
x=π+2nπ
D
x=3π/2+2nπ
39
For y=2sin(3x+π/6), amplitude=
A
3
B
2
C
π/6
D
6
40
For y=2sin(3x+π/6), period=
A
3
B
2π/3
C
π/6
D
6π
41
For y=2sin(3x+π/6), phase shift=
A
π/6 to the right
B
π/18 to the left
C
π/6 to the left
D
π/18 to the right
42
y=sin²x+cos²x=
A
0
B
2
C
1
D
sin2x
43
Range of y=secx excludes:
A
(−1,1)
B
(−∞,∞)
C
[−1,1]
D
0
44
y=cscx range:
A
(−1,1)
B
(−∞,∞)
C
[−1,1]
D
excludes (−1,1)
45
Period of y=2cos(4πx):
A
4π
B
1/2
C
4
D
π/2
46
Number of complete cycles of y=sin(3x) in [0,2π]:
A
1
B
2
C
3
D
6
47
The function y=sinx is:
A
Even
B
Odd
C
Neither
D
Both
48
The function y=cosx is:
A
Even
B
Odd
C
Neither
D
Both
49
The function y=tanx is:
A
Even
B
Odd
C
Neither
D
Both
50
y=sinx at x=π/6: y=
A
1
B
1/2
C
√3/2
D
√2/2
51
y=cosx at x=π/3: y=
A
1
B
1/2
C
√3/2
D
0
52
y=tanx at x=π/4: y=
A
0
B
1/2
C
1
D
√3
53
The graph of y=sin2x completes in [0,π]:
A
One cycle
B
Two cycles
C
Half cycle
D
Quarter cycle
54
The y-intercept of y=sinx is:
A
1
B
0
C
−1
D
π
55
The y-intercept of y=cosx is:
A
0
B
1
C
−1
D
π
56
The y-intercept of y=tanx is:
A
0
B
1
C
−1
D
undefined
57
Which is true about y=sinx and y=sin(x+2π)?
A
They are different
B
They are the same (period 2π)
C
y=sin(x+2π) is shifted
D
They are reflections
58
Horizontal compression of y=sinx by factor 2 gives:
A
y=sin(x/2)
B
y=sin(2x)
C
y=2sinx
D
y=sinx/2
59
Horizontal stretch of y=sinx by factor 2 gives:
A
y=sin(2x)
B
y=sin(x/2)
C
y=2sinx
D
y=sinx/2
60
Vertical stretch of y=cosx by factor 3:
A
y=cos(3x)
B
y=cos(x/3)
C
y=3cosx
D
y=(1/3)cosx
61
The graph of y=2sinx+1:
A
Amplitude=2, vertical shift up 1
B
Amplitude=1, shift 2
C
Amplitude=2, shift down 1
D
No amplitude
62
A function with period T satisfies f(x+T)=
A
0
B
f(x)
C
f(x)+T
D
f(T)
63
Which trig function has no amplitude (unbounded)?
A
sinx
B
cosx
C
tanx
D
None
64
sin(x+π) =
A
sinx
B
−sinx
C
cosx
D
−cosx
65
cos(x+π) =
A
cosx
B
−cosx
C
sinx
D
−sinx
66
sin(x+π/2) =
A
sinx
B
cosx
C
−sinx
D
−cosx
67
The graph of y=cscx can be drawn using:
A
y=sinx (reciprocal)
B
y=cosx
C
y=tanx
D
y=cotx
68
Period of y=|sinx| (absolute value):
A
2π
B
π
C
π/2
D
4π
69
The function y=sin(x) has exactly how many zeros in [0,2π]?
A
1
B
2
C
3
D
4
70
y=cos(nπx) for n=2: period =
A
1
B
2
C
1/2
D
4
71
For y=A sin(Bx+C)+D, D determines:
A
Amplitude
B
Period
C
Phase shift
D
Vertical shift (midline)
72
The maximum value of y=5sin(3x)−2:
A
5
B
3
C
−7
D
Both A. and C. are equivalent to 5 and −7
73
Minimum of y=5sin(3x)−2:
A
−7
B
−5
C
2
D
−2
74
The zeros of y=cos(2x) in [0,π] are at:
A
x=π/2
B
x=π/4 and 3π/4
C
x=0 and π
D
x=π/2 only
75
y=tan²x−sec²x =
A
−1
B
1
C
0
D
tanx
76
Range of y=sin(x)+cos(x):
A
[−1,1]
B
[−√2,√2]
C
(−√2,√2)
D
[0,√2]
77
The highest point on y=sin(x)+cos(x):
A
1
B
2
C
√2
D
√3
78
Period of y=sinx+cosx (which = √2 sin(x+π/4)):
A
π
B
2π
C
π/2
D
4π
79
y=sin(x)cos(x) = ?
A
sin(2x)/2
B
sin(2x)
C
2sin(2x)
D
sin(x)/2
80
Period of y=sinxcosx:
A
π
B
2π
C
π/2
D
4π
81
y=cos²x = ?
A
(1+cos2x)/2
B
(1−cos2x)/2
C
cos(2x)
D
1/2
82
Period of y=cos²x:
A
π
B
2π
C
π/2
D
4π
0
/ 83 answered
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