Math002
EXAM II
Term 123
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1) The number of vertical asymptotes of y = sec( 1 x + π ) over the 2
3
interval [ π , 13π ] is :
3
3
A) 3
B) 2
C) 4 D) 1
E) 5
2) The graph of y = tan(x + π ) over the interval (-π , π ) intersects the
4
x- axis at:
A) - π and 3π
4
4
B) - 3π and π
4
4
C) - π and π
4
4
D) - π and π
2
2
E) - π and π
2
4
Math002
EXAMI I
Term 123
3) If 270∘ < x < 360∘ , then
A) cscx = - 1- cos2x
1 - cos2 x
1 - cos2x
B) csc x = 1 - cos2 x
C) cscx = - 1+ cos2x D) csc x = - 1 + cos2 x
1 - cos x
E) csc x = - 1 + sin2 x
4) The range of f (x) = -2 + 6sin2x - 8cos2x is :
A) [-12 , 8]
B) [-10 , 10] C) [-10 , 8]
D) [-10, -2 ] E) [-2 , 8]
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Math002
EXAMI I
Term 123
5) tan x - cot x
is identical to :
sinx cosx
A) sec2 x - csc2 x
B) tan2 x + cot2x
C) sec2 x - tan2x D) sin2 x - cos2x
E) sec2 x + csc2x
6) Which one of the following statements is FALSE?
A) sinx + 1 2 - sinx - 1 2 =2x
B) sin(2.5) is a positive number
C) cos2 x = cosx
D) sin x - sin3x = sinx cos2 x E) cos4 x - 1 = - sin2x (cos2 x + 1)
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Math002
EXAMI I
Term 123
7) sin(270∘- θ) =
A) -cosθ B) sinθ
C) - tanθ
D) - cotθ
E) undefined
8) If tan t = - 4 , t in QII, and tan x = 5 , x in QIII , then
12
3
cot(t - x ) is equal to:
A) - 16
63
B) - 36
77
C) - 63
15
D) 63
36
E) - 12
36
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Math002
EXAMI I
Term 123
9) sin2 (67.5 ∘) - 1
2
A) 2
4
B) - 2
2
C) 2
D) 1
4
E) - 3
4
10) If sin x = - 4 , π < x < 3π , then cos x equals to :
2
5
2
A) - 5
5
B) 5
5
C) 5
D) - 1
5
E) 1
5
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Math002
EXAMI I
Term 123
11) The exact value of sec[ sin-1 ( - 4 ) - tan-1 ( - 5 )] =
5
12
A) 65
56
B) 65
63
C) 65
33
D) 33
63
E) 65
16
12) Which one of the following statements is TRUE ?
A) cos-1(cos 3 ) = 3
B) sin-1 (sin π ) = π
C) csc-1 x= 1
sin-1x
D) sin(sin-1π) = π
E) y = cos-1 x is an even function.
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Math002
EXAMI I
Term 123
13) The sum of the solutions of the equation over the interval [0,2π)
2sinx -1 = cscx is :
A) 7π
2
B) 3π
C) 3π
2
D) 15π
3
E) 5π
3
14) The number of solutions of the equation :
4 sin x cos x = 3 , 0 ≤ x < 2π is :
A) 4
B) 2
C) 3
D) 1
E) 5
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Math002
EXAMI I
Term 123
15) If x = 2 csc-1(
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y + 3
) , then y =
2
A) 2 csc ( x ) - 3
2
B) 3 csc ( x ) - 2
2
C) 1 csc ( x ) - 3 2
2
2
D) 2 csc (2x) - 3
E) 3 csc (2x) - 2 16) For 0 < x < 3π , the graph of the function y = 3 csc(x - π ) is increasing on
2
2
2
the interval(s):
A) (π , 3π )
2
B) (0 , π )
2
C) ( π , π )
2
D) (0 , π )
E) ( π , 3π )
2 2
Math002
EXAMI I
Term 123
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17) The exact value of cos(50∘)cos(50∘) + cos(40∘)sin(50∘) is equal to:
A) 1
B) 0
C) -1
D) 1
2
E) 2
2
18) If arctan x = arccos 12 , then x =
13
A) 5
12
B) 12
5
C) 12
13
D) 5 13
E) 13 12
Math002
EXAMI I
Term 123
=
19) 2 tan x
1 + tan2x
A) sin 2x
B) cos 2x
C) sec 2x
D) cot 2x
E) tan 2x
20) If cos-1x + sin-1 3 = π , then x =
2
2
A) 3
2
B) 2 2
C) 3 2
D) 2
E) 3
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