MATH 002
EXAM II
Summer Term-143
1) If csc
2)
is in the fourth quadrant then, sin
= -3 and
A)
8-2 2
9
B)
2 2 + 8
9
C)
8
D)
2 2
E)
10
-
B)
C)
D)
E)
3
3
6
6
11
6
+ cos
sec
=
2 2
-
8
- 10
If 3 sin 2x - 3 3 cos 2x = k sin 2x +
is equal to:
A)
Page 1
Code 02
, where k > 0 and 0 < x < 2
then
MATH 002
EXAM II
Summer Term-143
3) The sum of all the solutions of the equation
2sin x = 2cos 2x over the interval 0 , 2 ), is equal to:
A)
5
2
B)
5
6
C)
7
2
D)
E)
4) For
2
7
-
x
3
, the graph of the function y = - 2 cos 3x, lies below the
x-axis in the interval
A)
0,
B)
-
C)
-
D)
-
E)
Page 2
Code 02
3
3
,
6
6
, 0
,-
3
,
,
3
6
6
2
3
,
3
6
2
,
,
6
MATH 002
EXAM II
Summer Term-143
5) The exact value of cos 130° cos 65°
A)
- 6
4
B)
2
C)
6+ 2
D)
- 6- 2
4
0
E)
6) cos tan-1 5 - cot-1 3 =
12
4
A)
B)
C)
D)
E)
-
16
65
36
65
63
65
16
65
56
65
- sin 130° sin 65°
Page 3
Code 02
is
MATH 002
EXAM II
Summer Term-143
7) The solution set of the equation arc sin x + arc tan
A)
no real number
B)
a positive irrational number
C)
a negative rational number
D)
a positive rational number
E)
a negative irrational number
8) 1 cot x
2
2
-1
tan x =
2
2
A)
B)
csc x
cot x
C)
- cot x
D)
- tan x
E)
tan x
Page 4
Code 02
3 =
3
contains:
MATH 002
EXAM II
Summer Term-143
9) The graph of y = sec 2x +
A)
,
12 3
, 13
12 12
C)
,
, 13
12 12
12
12
D)
E)
3
,
3
< x < 13 is decreasing over the intervals
12
12
, 13
6
12
B)
12 3
,
,
6
,7
12 12
10) Which one of the following statements is TRUE for the function
y = tan-1 x?
A)
The range is 0,
B)
The y-intercept is
C)
D)
The domain is - ,
It is a decreasing function.
tan-1 - 3 =
3
6
E)
Page 5
Code 02
2
MATH 002
EXAM II
Summer Term-143
Page 6
Code 02
11) If u is a vector with magnitude 5, direction angle 120° and v = 4 3 i - 3j, then
the vertical component of the vector w = 4 u - 3 v is:
A)
B)
C)
D)
E)
7 3
- 22
13 3
- 13 3
-7 3
12) The number of vertical asymptotes of the graph of y = 3 tan
interval 0, 6 is
A)
B)
C)
D)
E)
three
six
four
two
five
2
x+
over the
MATH 002
13)
sec2
A)
- 2sec
Page 7
Code 02
1 + sin
1
B)
sin
+1
C)
1 - sin
1 + sin
D)
1 + cos
E)
1 - cos
1 + sin
14) For
tan
EXAM II
Summer Term-143
+ tan2 =
-
5
x
, the graph of y = 3 - 4 sin 5 x +
5
2
has
{Hint: Sketch the graph}
A)
B)
C)
D)
E)
three maximum values and three x-intercepts.
four maximum values and four x-intercepts.
four maximum values and two x-intercepts.
two maximum values and two x-intercepts.
two maximum values and four x-intercepts.
MATH 002
EXAM II
Summer Term-143
15) The exact value of cot
A)
B)
12
is equal to:
2- 3
-2-
3
C)
3+ 3
3
D)
3-2
E)
2+ 3
16) If a, b is the solution of the system of equations:
1
+ 1 = 1
x+2
y
1
x+2
-
A)
19
3
B)
6
5
2
C)
-
D)
-1
E)
1
5
2
1
y
=
-3
then a + b =
Page 8
Code 02
MATH 002
EXAM II
Summer Term-143
17) If cos2 = 4 and 90° <
5
A)
1
2
B)
-3
C)
-1
D)
-4
E)
-3
< 180° , then tan
Page 9
Code 02
=
10
10
3
3
18) If 0 < x <
2
, then sin x in terms of cot x is equal to:
A)
1 - cot2 x
1 - cot2 x
B)
cot2 x - 1
cot2 x - 1
C)
1 + cot2 x
1 + cot2 x
D)
1 + cot2 x
cot x
E)
1 - tan2 x
1 - tan2 x
MATH 002
EXAM II
Summer Term-143
19) The number of solutions of the equation csc2
0° , 360° ) is:
20)
A)
B)
5
4
C)
3
D)
1
E)
2
sin2
A)
B)
C)
D)
E)
(1 + cot ) + cos 2
- sec2
2 + cot2
cot
csc2
tan2
Page 10
Code 02
- 2cot
(1 - tan ) + cot2 =
= 0 over the interval